Relevant bibliographies by topics / Graphs, planar graphs, five color theorem / Journal articles
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Journal articles on the topic 'Graphs, planar graphs, five color theorem'

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Published: 24 April 2022
Last updated: 30 July 2025

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1

Liang, Zuosong, and Huandi Wei. "A Linear-Time Algorithm for 4-Coloring Some Classes of Planar Graphs." Computational Intelligence and Neuroscience 2021 (October 5, 2021): 1–5. http://dx.doi.org/10.1155/2021/7667656.

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Every graph G = V , E considered in this paper consists of a finite set V of vertices and a finite set E of edges, together with an incidence function that associates each edge e ∈ E of G with an unordered pair of vertices of G which are called the ends of the edge e . A graph is said to be a planar graph if it can be drawn in the plane so that its edges intersect only at their ends. A proper k -vertex-coloring of a graph G = V , E is a mapping c : V ⟶ S ( S is a set of k colors) such that no two adjacent vertices are assigned the same colors. The famous Four Color Theorem states that a planar
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2

BOWLIN, GARRY, and MATTHEW G. BRIN. "COLORING PLANAR GRAPHS VIA COLORED PATHS IN THE ASSOCIAHEDRA." International Journal of Algebra and Computation 23, no. 06 (2013): 1337–418. http://dx.doi.org/10.1142/s0218196713500276.

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Hassler Whitney's theorem of 1931 reduces the task of finding proper, vertex 4-colorings of triangulations of the 2-sphere to finding such colorings for the class ℌ of triangulations of the 2-sphere that have a Hamiltonian circuit. This has been used by Whitney and others from 1936 to the present to find equivalent reformulations of the 4 Color Theorem (4CT). Recently there has been activity to try to use some of these reformulations to find a shorter proof of the 4CT. Every triangulation in ℌ has a dual graph that is a union of two binary trees with the same number of leaves. Elements of a gr
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3

Bhapkar, H. R., and J. N. Salunke. "Proof of Four Color Map Theorem by Using PRN of Graph." Bulletin of Society for Mathematical Services and Standards 11 (September 2014): 26–30. http://dx.doi.org/10.18052/www.scipress.com/bsmass.11.26.

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This paper intends to study the relation between PRN and chromatic number of planar graphs. In this regard we investigate that isomorphic or 1 isomorphic graph may or may not have equal PRN and few other related results. Precisely, we give simple proof of Four Color Map Theorem.
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4

XUE, NINI, and BAOYINDURENG WU. "LIST POINT ARBORICITY OF GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 02 (2012): 1250027. http://dx.doi.org/10.1142/s1793830912500279.

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Let G be a graph. The point arboricity of G, denoted by ρ(G), is the minimum number of colors that can be used to color the vertices of G so that each color class induces an acyclic subgraph of G. Borodin et al. (Discrete Math.214 (2000) 101–112) first introduced the list point arboricity of G, denoted by ρl(G). We prove that for any graph G, [Formula: see text], where deg (G) denotes the degeneracy of G, that is, the minimum number k such that δ(H) ≤ k for any subgraph H of G. Using this upper bound, we show that ρl(G) ≤ 3 for any planar graph G. In particular, if either G is K4-minor free, o
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5

Felsner, Stefan, Hendrik Schrezenmaier, and Raphael Steiner. "Pentagon Contact Representations." Electronic Journal of Combinatorics 25, no. 3 (2018). http://dx.doi.org/10.37236/7216.

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Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or of a set of internally disjoint homothetic squares have received quite some attention in recent years. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly such a representation exists for every triangulation whose outer face is a $5$-gon. We relate these representations to five color forests. These combinatorial structures resemble Schnyder woods and transversal structures, respe
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6

Zhang, Xuanhan. "Attempts and Inferences of the Four-Color Theorem." Science and Technology of Engineering, Chemistry and Environmental Protection 1, no. 10 (2024). https://doi.org/10.61173/xgertb46.

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The Four-Color Theorem is a classic problem in graph theory, stating that any planar map can be colored using no more than four colors so that no adjacent regions share the same color. Since 1976, when Appel and Haken used computer assistance to prove this theorem, it has been considered solved. However, due to its complexity and the difficulty of manually verifying the proof, some mathematicians still have doubts. This study proposes a new logical approach to provide an alternative proof for the Four-Color Theorem. Using a combination of theoretical derivations and graph theory tools, the pap
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7

Axenovich, Maria, Ursula Schade, Carsten Thomassen, and Torsten Ueckerdt. "Planar Ramsey Graphs." Electronic Journal of Combinatorics 26, no. 4 (2019). http://dx.doi.org/10.37236/8366.

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We say that a graph $H$ is planar unavoidable if there is a planar graph $G$ such that any red/blue coloring of the edges of $G$ contains a monochromatic copy of $H$, otherwise we say that $H$ is planar avoidable. That is, $H$ is planar unavoidable if there is a Ramsey graph for $H$ that is planar. It follows from the Four-Color Theorem and a result of Gonçalves that if a graph is planar unavoidable then it is bipartite and outerplanar. We prove that the cycle on $4$ vertices and any path are planar unavoidable. In addition, we prove that all trees of radius at most $2$ are planar unavoidable
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8

Aboulker, Pierre, Marthe Bonamy, Nicolas Bousquet, and Louis Esperet. "Distributed Coloring in Sparse Graphs with Fewer Colors." Electronic Journal of Combinatorics 26, no. 4 (2019). http://dx.doi.org/10.37236/8395.

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This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar graphs can be colored with at most 4 colors, and the proof gives a (sequential) quadratic algorithm finding such a coloring. A natural problem is to improve this complexity in the distributed setting. Using the fact that planar graphs contain linearly many vertices of degree at most 6, Goldberg, Plotkin, and Shannon obtained a deterministic distributed algorithm coloring $n$-vertex planar graphs with 7 colors in $O(\lo
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9

Voigt, Margit, and Arnfried Kemnitz. "A Note on Not-4-List Colorable Planar Graphs." Electronic Journal of Combinatorics 25, no. 2 (2018). http://dx.doi.org/10.37236/7320.

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The Four Color Theorem states that every planar graph is properly 4-colorable. Moreover, it is well known that there are planar graphs that are non-$4$-list colorable. In this paper we investigate a problem combining proper colorings and list colorings. We ask whether the vertex set of every planar graph can be partitioned into two subsets where one subset induces a bipartite graph and the other subset induces a $2$-list colorable graph. We answer this question in the negative strengthening the result on non-$4$-list colorable planar graphs.
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10

Dębski, Michał, Piotr Micek, Felix Schröder, and Stefan Felsner. "Improved Bounds for Centered Colorings." Advances in Combinatorics, August 16, 2021. http://dx.doi.org/10.19086/aic.27351.

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A vertex coloring $\phi$ of a graph $G$ is $p$-centered if for every connected subgraph $H$ of $G$ either $\phi$ uses more than $p$ colors on $H$ or there is a color that appears exactly once on $H$. Centered colorings form one of the families of parameters that allow to capture notions of sparsity of graphs: A class of graphs has bounded expansion if and only if there is a function $f$ such that for every $p\geq1$, every graph in the class admits a $p$-centered coloring using at most $f(p)$ colors. In this paper, we give upper bounds for the maximum number of colors needed in a $p$-centered c
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11

Schauz, Uwe. "Colorings and Orientations of Matrices and Graphs." Electronic Journal of Combinatorics 13, no. 1 (2006). http://dx.doi.org/10.37236/1087.

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We introduce colorings and orientations of matrices as generalizations of the graph theoretic terms. The permanent per$(A[\zeta|\xi])$ of certain copies $A[\zeta|\xi]$ of a matrix $A$ can be expressed as a weighted sum over the orientations or the colorings of $A$. When applied to incidence matrices of graphs these equations include Alon and Tarsi's theorem about Eulerian orientations and the existence of list colorings. In the case of planar graphs we deduce Ellingham and Goddyn's partial solution of the list coloring conjecture and Scheim's equivalency between not vanishing permanents and th
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12

Foucaud, Florent, Reza Naserasr, and Rongxing Xu. "Extended Double Covers and Homomorphism Bounds of Signed Graphs." Electronic Journal of Combinatorics 30, no. 3 (2023). http://dx.doi.org/10.37236/10754.

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A signed graph $(G, \sigma)$ is a graph $G$ together with an assignment $\sigma:E(G) \rightarrow \{+,-\}$. The notion of homomorphisms of signed graphs is a relatively new development which allows to strengthen the connection between the theories of minors and colorings of graphs. Following this thread of thoughts, we investigate this connection through the notion of Extended Double Covers of signed graphs, which was recently introduced by Naserasr, Sopena and Zaslavsky. More precisely, we say that a signed graph $(B, \pi)$ is planar-complete if any signed planar graph $(G, \sigma)$ which veri
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13

Cranston, Daniel W., and Landon Rabern. "Planar Graphs have Independence Ratio at least 3/13." Electronic Journal of Combinatorics 23, no. 3 (2016). http://dx.doi.org/10.37236/5309.

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The 4 Color Theorem (4CT) implies that every $n$-vertex planar graph has an independent set of size at least $\frac{n}4$; this is best possible, as shown by the disjoint union of many copies of $K_4$. In 1968, Erdős asked whether this bound on independence number could be proved more easily than the full 4CT. In 1976 Albertson showed (independently of the 4CT) that every $n$-vertex planar graph has an independent set of size at least $\frac{2n}9$. Until now, this remained the best bound independent of the 4CT. Our main result improves this bound to $\frac{3n}{13}$.
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14

Fulek, Radoslav, Jan Kynčl, Igor Malinović, and Dömötör Pálvölgyi. "Clustered Planarity Testing Revisited." Electronic Journal of Combinatorics 22, no. 4 (2015). http://dx.doi.org/10.37236/5002.

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The Hanani–Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward extension to flat clustered graphs with three or more disjoint clusters is not possible. For general clustered graphs we show a variant of the Hanani–Tutte theorem in the case when each cluster induces a connected subgraph.Di Battista and Frati prove
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15

Postle, Luke, and Evelyne Smith-Roberge. "Local Girth Choosability of Planar Graphs." Advances in Combinatorics, December 16, 2022, 1–38. http://dx.doi.org/10.19086/aic.2022.8.

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In 1994, Thomassen famously proved that every planar graph is 5-choosable, resolving a conjecture initially posed by Vizing and, independently, Erd˝os, Rubin, and Taylor in the 1970s. Later, Thomassen proved that every planar graph of girth at least five is 3-choosable. In this paper, we introduce the concept of a local girth list assignment: a list assignment wherein the list size of a vertex depends not on the girth of the graph, but rather on the length of the shortest cycle in which the vertex is contained. We give a local list colouring theorem unifying the two theorems of Thomassen menti
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16

Choi, Hojin, and Young Soo Kwon. "On $t$-Common List-Colorings." Electronic Journal of Combinatorics 24, no. 3 (2017). http://dx.doi.org/10.37236/6738.

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In this paper, we introduce a new variation of list-colorings. For a graph $G$ and for a given nonnegative integer $t$, a $t$-common list assignment of $G$ is a mapping $L$ which assigns each vertex $v$ a set $L(v)$ of colors such that given set of $t$ colors belong to $L(v)$ for every $v\in V(G)$. The $t$-common list chromatic number of $G$ denoted by $ch_t(G)$ is defined as the minimum positive integer $k$ such that there exists an $L$-coloring of $G$ for every $t$-common list assignment $L$ of $G$, satisfying $|L(v)| \ge k$ for every vertex $v\in V(G)$. We show that for all positive integer
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17

Kierstead, H. A., Alexandr Kostochka, and Zimu Xiang. "Equitable List Coloring of Planar Graphs With Given Maximum Degree." Journal of Graph Theory, December 15, 2024. https://doi.org/10.1002/jgt.23203.

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ABSTRACTIf is a list assignment of colors to each vertex of an ‐vertex graph , then an equitable ‐coloring of is a proper coloring of vertices of from their lists such that no color is used more than times. A graph is equitably ‐choosable if it has an equitable ‐coloring for every ‐list assignment . In 2003, Kostochka, Pelsmajer, and West (KPW) conjectured that an analog of the famous Hajnal–Szemerédi Theorem on equitable coloring holds for equitable list coloring, namely, that for each positive integer every graph with maximum degree at most is equitably ‐choosable. The main result of this pa
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18

Albertson, Michael O., and Joan P. Hutchinson. "Graph Color Extensions: When Hadwiger's Conjecture and Embeddings Help." Electronic Journal of Combinatorics 9, no. 1 (2002). http://dx.doi.org/10.37236/1653.

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Suppose $G$ is $r$-colorable and $P \subseteq V(G)$ is such that the components of $G[P]$ are far apart. We show that any $(r+s)$-coloring of $G[P]$ in which each component is $s$-colored extends to an $(r+s)$-coloring of $G$. If $G$ does not contract to $K_5$ or is planar and $s \geq 2$, then any $(r+s-1)$-coloring of $P$ in which each component is $s$-colored extends to an $(r+s-1)$-coloring of $G$. This result uses the Four Color Theorem and its equivalence to Hadwiger's Conjecture for $k = 5$. For $s=2$ this provides an affirmative answer to a question of Thomassen. Similar results hold fo
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19

Beccaria, M., S. Giombi, and A. A. Tseytlin. "Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM." Journal of High Energy Physics 2022, no. 1 (2022). http://dx.doi.org/10.1007/jhep01(2022)056.

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Abstract Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the $$ \mathcal{N} $$ N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilso
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20

Holliday, Sarah, Jennifer Vandenbussche, and Erik E. Westlund. "Completing Partial Proper Colorings using Hall's Condition." Electronic Journal of Combinatorics 22, no. 3 (2015). http://dx.doi.org/10.37236/4387.

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In the context of list-coloring the vertices of a graph, Hall's condition is a generalization of Hall's Marriage Theorem and is necessary (but not sufficient) for a graph to admit a proper list-coloring. The graph $G$ with list assignment $L$ satisfies Hall's condition if for each subgraph $H$ of $G$, the inequality $|V(H)| \leq \sum_{\sigma \in \mathcal{C}} \alpha(H(\sigma, L))$ is satisfied, where $\mathcal{C}$ is the set of colors and $\alpha(H(\sigma, L))$ is the independence number of the subgraph of $H$ induced on the set of vertices having color $\sigma$ in their lists. A list assignmen
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21

Henry, Garrett. "New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Path-Cut As Hyper Eulogy-Path-Cut On Super EULA-Path-Cut." April 7, 2023. https://doi.org/10.5281/zenodo.7809358.

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\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % li
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Spin On Super Spacy." March 10, 2023. https://doi.org/10.13140/RG.2.2.33028.40321.

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“#187 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Spin On Super Spacy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33028.40321). @ResearchGate: https://www.researchgate.net/publication/369118224 @Scribd: https://www.scribd.com/document/630547839 @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amss
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23

Henry, Garrett. "Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer's Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs." January 17, 2023. https://doi.org/10.20944/preprints202301.0308.v1.

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Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer’s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs January 2023 DOI: 10.20944/preprints202301.0308.v1 License: CC BY 4.0 — Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer’s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs — “New Publication” & “New Citation”  #PublishingDay #Publish — Article #126 January 2023 DOI: 10.20944
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark." March 8, 2023. https://doi.org/10.13140/RG.2.2.21756.21129.

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“#184 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark”, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). @ResearchGate: https://www.researchgate.net/publication/369086888 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, grap
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Henry, Garrett. "New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer's Recognition With (Extreme) SuperHyperGraph." March 8, 2023. https://doi.org/10.13140/RG.2.2.30983.68009.

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“#183 Article” Henry Garrett, “New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer's Recognition With (Extreme) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). @ResearchGate: https://www.researchgate.net/publication/369087468 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, gra
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By List-Coloring As Hyper List On Super Lisle." March 9, 2023. https://doi.org/10.13140/RG.2.2.21389.20966.

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\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % li
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Henry, Garrett. "New Ideas On Super Lith By Hyper Lite Of List-Coloring In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 9, 2023. https://doi.org/10.13140/RG.2.2.16356.04489.

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“#185 Article” Henry Garrett, “New Ideas On Super Lith By Hyper Lite Of List-Coloring In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.16356.04489). @ResearchGate: https://www.researchgate.net/publication/369113233 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssy
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Clique-Cut As Hyper Click On Super Cliche." March 11, 2023. https://doi.org/10.13140/RG.2.2.26134.01603.

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“#188 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Clique-Cut As Hyper Click On Super Cliche”, ResearchGate 2023, (doi: 10.13140/RG.2.2.26134.01603). @ResearchGate: https://www.researchgate.net/publication/369147477 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bo
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Henry, Garrett. "New Ideas On Super Cliff By Hyper Cling Of Clique-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 11, 2023. https://doi.org/10.13140/RG.2.2.27392.30721.

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“#188 Article” Henry Garrett, “New Ideas On Super Cliff By Hyper Cling Of Clique-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.27392.30721). @ResearchGate: https://www.researchgate.net/publication/369151536 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssym
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Henry, Garrett. "New Ideas On Super Decompensation By Hyper Decompress Of Clique-Decompositions In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 13, 2023. https://doi.org/10.13140/RG.2.2.27169.48487.

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Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Clique-Decompositions In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.27169.48487). @ResearchGate: https://www.researchgate.net/publication/369186444 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssy
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Clique-Decompositions As Hyper Decompile On Super Decommission." March 13, 2023. https://doi.org/10.13140/RG.2.2.18780.87683.

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“#191 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Clique-Decompositions As Hyper Decompile On Super Decommission”, ResearchGate 2023, (doi: 10.13140/RG.2.2.18780.87683). @ResearchGate: https://www.researchgate.net/publication/369187021 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, a
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Henry, Garrett. "New Ideas On Super Nebulizer By Hyper Nub Of Clique-Neighbors In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 13, 2023. https://doi.org/10.13140/RG.2.2.29764.71046.

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“#192 Article” Henry Garrett, “New Ideas On Super Nebulizer By Hyper Nub Of Clique-Neighbors In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.29764.71046). @ResearchGate: https://www.researchgate.net/publication/369196478 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Clique-Neighbors As Hyper Nebbish On Super Nebulous." March 13, 2023. https://doi.org/10.13140/RG.2.2.36475.59683.

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“#193 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Clique-Neighbors As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.36475.59683). @ResearchGate: https://www.researchgate.net/publication/369196398 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts
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Henry, Garrett. "New Ideas On Super Stale By Hyper Stalk Of Stable-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 14, 2023. https://doi.org/10.13140/RG.2.2.20170.24000.

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“#194 Article” Henry Garrett, “New Ideas On Super Stale By Hyper Stalk Of Stable-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.20170.24000). @ResearchGate: https://www.researchgate.net/publication/369214553 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/98524637   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts,
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Cut As Hyper Stain On Super Stagy." March 14, 2023. https://doi.org/10.13140/RG.2.2.23525.68320.

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“#195 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Cut As Hyper Stain On Super Stagy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23525.68320). @ResearchGate: https://www.researchgate.net/publication/369211168 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb,
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Decompositions As Hyper Stain On Super Stagy." March 15, 2023. https://doi.org/10.13140/RG.2.2.23423.28327.

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“#197 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Decompositions As Hyper Stain On Super Stagy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23423.28327). @ResearchGate: https://www.researchgate.net/publication/369245279 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfo
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Henry, Garrett. "New Ideas On Super Stale By Hyper Stalk Of Stable-Decompositions In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 15, 2023. https://doi.org/10.13140/RG.2.2.28456.44805.

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“#196 Article” Henry Garrett, “New Ideas On Super Stale By Hyper Stalk Of Stable-Decompositions In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.28456.44805). @ResearchGate: https://www.researchgate.net/publication/369245643 @Scribd: https://www.scribd.com/document/631525857 @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/98569557   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsth
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns." March 6, 2023. https://doi.org/10.13140/RG.2.2.31147.52003.

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“#178 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). @ResearchGate: https://www.researchgate.net/publication/369029627 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfont
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Henry, Garrett. "New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 6, 2023. https://doi.org/10.13140/RG.2.2.32825.24163.

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“#177 Article” Henry Garrett, “New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). @ResearchGate: https://www.researchgate.net/publication/369030046 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/98024333   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, a
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Neighbor As Hyper Nebbish On Super Nebulous." March 16, 2023. https://doi.org/10.13140/RG.2.2.31025.45925.

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“#199 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Neighbor As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31025.45925). @ResearchGate: https://www.researchgate.net/publication/369274134 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfon
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Henry, Garrett. "New Ideas On Super Nebulizer By Hyper Nub Of Stable-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 16, 2023. https://doi.org/10.13140/RG.2.2.17184.25602.

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“#196 Article” Henry Garrett, “New Ideas On Super Nebulizer By Hyper Nub Of Stable-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.17184.25602). @ResearchGate: https://www.researchgate.net/publication/369284173 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfon
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Cut As Hyper Vertu On Super Vertigo." March 17, 2023. https://doi.org/10.13140/RG.2.2.24288.35842.

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“#201 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Cut As Hyper Vertu On Super Vertigo”, ResearchGate 2023, (doi: 10.13140/RG.2.2.24288.35842). @ResearchGate: https://www.researchgate.net/publication/369322064 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/-   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb
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Henry, Garrett. "New Ideas On Super Vertigo By Hyper Vertu Of Vertex-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 17, 2023. https://doi.org/10.13140/RG.2.2.32467.25124.

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#200 Article” Henry Garrett, “New Ideas On Super Vertigo By Hyper Vertu Of Vertex-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.32467.25124). @ResearchGate: https://www.researchgate.net/publication/369327937 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   \documentclass[10pt,letterpaper]{art
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Decomposition As Hyper Decompress On Super Decompensation." March 18, 2023. https://doi.org/10.13140/RG.2.2.30212.81289.

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“#203 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Decomposition As Hyper Decompress On Super Decompensation”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30212.81289). @ResearchGate: https://www.researchgate.net/publication/369335397 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd,
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Henry, Garrett. "New Ideas On Super Decompensation By Hyper Decompress Of Vertex-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 18, 2023. https://doi.org/10.13140/RG.2.2.18468.76169.

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“#202 Article” Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Vertex-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.18468.76169). @ResearchGate: https://www.researchgate.net/publication/369340345 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   -- \doc
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Neighbor As Hyper Nebbish On Super Nebulous." March 19, 2023. https://doi.org/10.13140/RG.2.2.31366.24641.

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“#205 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Neighbor As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31366.24641). @ResearchGate: https://www.researchgate.net/publication/369365026 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   \documentclass[10pt,lett
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Henry, Garrett. "New Ideas On Super Nebulous By Hyper Nebbish Of Vertex-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 19, 2023. https://doi.org/10.13140/RG.2.2.34721.68960.

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“#204 Article” Henry Garrett, “New Ideas On Super Nebulous By Hyper Nebbish Of Vertex-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.34721.68960). @ResearchGate: https://www.researchgate.net/publication/369365539 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   -- \documentclass[10p
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Cut As Hyper Edify On Super Eddy." March 20, 2023. https://doi.org/10.13140/RG.2.2.11377.76644.

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“#207 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Cut As Hyper Edify On Super Eddy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.11377.76644). @ResearchGate: https://www.researchgate.net/publication/369374430 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/98839726 Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   \documentclass[10pt,letterpape
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Henry, Garrett. "New Ideas On Super Eddy By Hyper Edify Of Edge-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph." March 20, 2023. https://doi.org/10.13140/RG.2.2.23750.96329.

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“#206 Article” Henry Garrett, “New Ideas On Super Eddy By Hyper Edify Of Edge-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23750.96329). @ResearchGate: https://www.researchgate.net/publication/369374477 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   \documentclass[10pt,letterpaper]{a
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Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Decomposition As Hyper Decompress On Super Decompensation." March 21, 2023. https://doi.org/10.13140/RG.2.2.22545.10089.

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“#209 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Decomposition As Hyper Decompress On Super Decompensation”, ResearchGate 2023, (doi: 10.13140/RG.2.2.22545.10089). @ResearchGate: https://www.researchgate.net/publication/369385213 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/98896282 Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   &nbsp
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