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Journal articles on the topic 'The two color theorem'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Doi, H. "The "four-color issue" in ecology for considering ecosystem boundaries." Web Ecology 13, no. 1 (2013): 91–93. http://dx.doi.org/10.5194/we-13-91-2013.

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Abstract. Ecosystem boundaries are important structures in defining ecosystems. To date, ecologists have not extensively considered which boundaries are important in explaining ecological phenomena in order to simplify ecological theories. The four-color theorem in mathematics maintains that only four colors are required to color a set of regions so that no two adjacent regions have the same color. Before being proven in 1976, the theorem was considered the "four-color issue", which proposed that a small number of colors were required to separate regional boundaries. Applying the principle of

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2

White, Jacob Anthony. "Brooks' theorem for 2-fold coloring." Contributions to Discrete Mathematics 17, no. 2 (2022): 67–76. http://dx.doi.org/10.55016/ojs/cdm.v17i2.62707.

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The two-fold chromatic number of a graph is the minimum number of colors needed to ensure that there is a way to color the graph so that each vertex gets two distinct colors, and adjacent vertices have no colors in common. The Ore degree is the maximum sum of degrees of an edge in a graph. We prove that, for 2-connected graphs, the two-fold chromatic number is at most the Ore degree, unless G is a complete graph or an odd cycle.

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3

Goldstein, Larry, and Yosef Rinott. "Multivariate normal approximations by Stein's method and size bias couplings." Journal of Applied Probability 33, no. 1 (1996): 1–17. http://dx.doi.org/10.2307/3215259.

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Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any non-negative random vector. Theorem 1.2 requires multivariate size bias coupling, which we discuss in studying the approximation of distributions of sums of dependent random vectors. In the univariate case, we briefly illustrate this approach for certain sums of nonlinear functions of multivariate normal variables. As a second illustration, we show that the multivariate distribution counting the number of vertices with given de

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Goldstein, Larry, and Yosef Rinott. "Multivariate normal approximations by Stein's method and size bias couplings." Journal of Applied Probability 33, no. 01 (1996): 1–17. http://dx.doi.org/10.1017/s0021900200103675.

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Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any non-negative random vector. Theorem 1.2 requires multivariate size bias coupling, which we discuss in studying the approximation of distributions of sums of dependent random vectors. In the univariate case, we briefly illustrate this approach for certain sums of nonlinear functions of multivariate normal variables. As a second illustration, we show that the multivariate distribution counting the number of vertices with given de

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5

Aletti, Giacomo, Caterina May, and Piercesare Secchi. "A central limit theorem, and related results, for a two-color randomly reinforced urn." Advances in Applied Probability 41, no. 3 (2009): 829–44. http://dx.doi.org/10.1239/aap/1253281065.

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We prove a central limit theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.

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6

Aletti, Giacomo, Caterina May, and Piercesare Secchi. "A central limit theorem, and related results, for a two-color randomly reinforced urn." Advances in Applied Probability 41, no. 03 (2009): 829–44. http://dx.doi.org/10.1017/s0001867800003578.

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We prove a central limit theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.

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7

Shen, Zhe, Yudong Ma, and Takeshi Tsuchiya. "Four-Dimensional Gait Surfaces for a Tilt-Rotor—Two Color Map Theorem." Drones 6, no. 5 (2022): 103. http://dx.doi.org/10.3390/drones6050103.

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This article presents the four-dimensional surfaces that guide the gait plan for a tilt-rotor. The previous gaits analyzed in the tilt-rotor research are inspired by animals; no theoretical base backs the robustness of these gaits. This research deduces the gaits by diminishing the adverse effect of the attitude of the tilt-rotor for the first time. Four-dimensional gait surfaces are subsequently found on which the gaits are expected to be robust to the attitude. These surfaces provide the region where the gait is suggested to be planned. However, a discontinuous region may hinder the gait pla

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8

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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9

Narendra, Risang. "Polinomial Kromatik Graf Bunga." Unisda Journal of Mathematics and Computer Science (UJMC) 8, no. 2 (2022): 55–58. http://dx.doi.org/10.52166/ujmc.v8i2.3713.

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In this study, the class of a graph called Flower Graph was discussed. Flower Graph is a special way in a graphic. A graph G is called a flower chart-. This graph will be symbolized by . Then, it is defined by a flower chart-, with the petal to which in a flower graph-, by -petal removed, for . Flower graphics-: with petal as much as is denoted by . Chromatic polynomial is the amount of forms to color the point in graph G with color, where there are no two points that fit to obtain the same color. In the end, using the reduction theorem, the chromatic polynomial theorem of the Sikel chart and

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Bhamare, Dr Megha Abhiman. "CHROMATIC NUMBER OPTIMIZATION FOR EFFICIENT MAP COLORING OF MAHARASHTRA'S DISTRICTS." International Journal of Engineering Applied Sciences and Technology 09, no. 06 (2024): 153–57. https://doi.org/10.33564/ijeast.2024.v09i06.020.

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This research explores the application of graph coloring algorithms to minimize the number of colors required for coloring the districts of Maharashtra, ensuring that no two adjacent districts share the same color. Using an adjacency matrix representation, where each district corresponds to a vertex and edges represent shared borders, the problem is framed as a graph coloring challenge. The primary objective is to demonstrate that a minimum of four colors suffice to color the entire map, in line with the Four Color Theorem, which asserts that any planar map can be colored with at most four col

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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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12

Kuba, Markus, and Henning Sulzbach. "On martingale tail sums in affine two-color urn models with multiple drawings." Journal of Applied Probability 54, no. 1 (2017): 96–117. http://dx.doi.org/10.1017/jpr.2016.89.

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AbstractIn two recent works, Kuba and Mahmoud (2015a) and (2015b) introduced the family of two-color affine balanced Pólya urn schemes with multiple drawings. We show that, in large-index urns (urn index between ½ and 1) and triangular urns, the martingale tail sum for the number of balls of a given color admits both a Gaussian central limit theorem as well as a law of the iterated logarithm. The laws of the iterated logarithm are new, even in the standard model when only one ball is drawn from the urn in each step (except for the classical Pólya urn model). Finally, we prove that the martinga

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13

Calude, Cristian S., and Elena Calude. "The complexity of the four colour theorem." LMS Journal of Computation and Mathematics 13 (August 27, 2010): 414–25. http://dx.doi.org/10.1112/s1461157009000461.

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AbstractThe four colour theorem states that the vertices of every planar graph can be coloured with at most four colours so that no two adjacent vertices receive the same colour. This theorem is famous for many reasons, including the fact that its original 1977 proof includes a non-trivial computer verification. Recently, a formal proof of the theorem was obtained with the equational logic program Coq [G. Gonthier, ‘Formal proof–the four color theorem’,Notices of Amer. Math. Soc.55 (2008) no. 11, 1382–1393]. In this paper we describe an implementation of the computational method introduced by

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14

Gyárfás, András, and Gábor N. Sárközy. "“Less” Strong Chromatic Indices and the (7, 4)-Conjecture." Studia Scientiarum Mathematicarum Hungarica 60, no. 2-3 (2023): 109–22. http://dx.doi.org/10.1556/012.2023.01539.

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A proper edge coloring of a graph 𝐺 is strong if the union of any two color classes does not contain a path with three edges (i.e. the color classes are induced matchings). The strong chromatic index 𝑞(𝐺) is the smallest number of colors needed for a strong coloring of 𝐺. One form of the famous (6, 3)-theorem of Ruzsa and Szemerédi (solving the (6, 3)-conjecture of Brown–Erdős–Sós) states that 𝑞(𝐺) cannot be linear in 𝑛 for a graph 𝐺 with 𝑛 vertices and 𝑐𝑛2 edges. Here we study two refinements of 𝑞(𝐺) arising from the analogous (7, 4)-conjecture. The first is 𝑞𝐴(𝐺), the smallest number of colo

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15

Gilchrist, M., та S. Shelah. "Identities on cardinals less than ℵω". Journal of Symbolic Logic 61, № 3 (1996): 780–87. http://dx.doi.org/10.2307/2275784.

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Let κ be an uncountable cardinal and the edges of a complete graph with κ vertices be colored with ℵ0 colors. For the Erdős-Rado theorem implies that there is an infinite monochromatic subgraph. However, if , then it may be impossible to find a monochromatic triangle. This paper is concerned with the latter situation. We consider the types of colorings of finite subgraphs that must occur when the edges of the complete graph on vertices are colored with ℵ0 colors. In particular, we are concerned with the case ℵ1 ≤ κ ≤ ℵω.The study of these color patterns (known as identities) has a history that

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Thodeti.Suresh, Dr. G. Srinivasu Prof. E. Kesava Reddy. "Verifying the Neighbouring k-edge Coloration Technique for Bipartite Graphs." Scandinavian Journal of Information Systems 35, no. 1 (2023): 727–32. https://doi.org/10.5281/zenodo.7807462.

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This paper focuses on verifying the neighbouring k-edge coloration technique for balancing multi-color problems in the bipartite graph. Thus, it eliminates triangular copies of similar colour shades while maintaining exactly two colours spacing between the edges. It is achieved by inducing bipartite color selections from two unique color sets say   and  . Thus, ensures the minimum colour interference exists by employing a fair version of the neighbouring k-edge colouring technique.  Theoretical evidence, theorems, and proofs are discussed, and results shows the superiority

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Gilchrist, Martin, та Saharon Shelah. "The consistency of ZFC + 2ℵ0 > ℵω + ℐ(ℵ2) = ℐ(ℵω)". Journal of Symbolic Logic 62, № 4 (1997): 1151–60. http://dx.doi.org/10.2307/2275632.

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Let κ be an uncountable cardinal and the edges of a complete graph with κ vertices be colored with ℵ0 colors. For the Erdős-Rado theorem implies that there is an infinite monochromatic subgraph. However, if , then it may be impossible to find a monochromatic triangle. This paper is concerned with the latter situation. We consider the types of colorings of finite subgraphs that must occur when . In particular, we are concerned with the case ℵ1 ≤ κ ≤ ℵω.The study of these color patterns (known as identities) has a history that involves the existence of compactness theorems for two cardinal model

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18

Bandyopadhyay, Antar, Svante Janson, and Debleena Thacker. "Strong convergence of infinite color balanced urns under uniform ergodicity." Journal of Applied Probability 57, no. 3 (2020): 853–65. http://dx.doi.org/10.1017/jpr.2020.37.

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AbstractWe consider the generalization of the Pólya urn scheme with possibly infinitely many colors, as introduced in [37], [4], [5], and [6]. For countably many colors, we prove almost sure convergence of the urn configuration under the uniform ergodicity assumption on the associated Markov chain. The proof uses a stochastic coupling of the sequence of chosen colors with a branching Markov chain on a weighted random recursive tree as described in [6], [31], and [26]. Using this coupling we estimate the covariance between any two selected colors. In particular, we re-prove the limit theorem fo

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19

Rauf, Dewi Nur Angriani, Novianita Achmad, and Nisky Imansyah Yahya. "Pewarnaan Pelangi pada Graf Garis dari Graf Ilalang (S_(3,r))." Griya Journal of Mathematics Education and Application 5, no. 1 (2025): 26–34. https://doi.org/10.29303/griya.v5i1.529.

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The rainbow connection number, denoted by rc(G), is the minimum number of colors required to color the edges of a graph G such that the graph is rainbow connected. A graph G is said to be rainbow connected if every pair of vertices in the graph has at least one rainbow path, a path in which each edge has a different color. Rainbow coloring has been extensively studied on various types of graphs and their modifications, including line graphs. The line graph L(G) of a graph is a graph whose vertex set is V(L(G)) = E(G), meaning each vertex in represents an edge of . Two vertices in L(G) are adja

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20

LI, GUODONG, LEQUAN MIN, and HONGYAN ZANG. "COLOR EDGE DETECTIONS BASED ON CELLULAR NEURAL NETWORK." International Journal of Bifurcation and Chaos 18, no. 04 (2008): 1231–42. http://dx.doi.org/10.1142/s0218127408020963.

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Color edge detection is one of the most important steps for RGB image recognition. In this paper, we first present two robustness design theorems for the Edgegray Detection Cellular Neural Network (EDGE CNN) and the counter detection (CD) CNN. Second, based on a color plane transform of RGB image and the two theorems, we design a color EDGE CNN and a CD CNN. As applications, the two CNNs detect successfully the edges of a standard color edge test pattern, and two popular RGB images, respectively. Our findings show that CNN may provide a useful tool for color image processing.

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CARLUCCI, LORENZO, and KONRAD ZDANOWSKI. "THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS." Journal of Symbolic Logic 79, no. 01 (2014): 89–102. http://dx.doi.org/10.1017/jsl.2013.27.

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Abstract We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called exactly large sets. An exactly large set is a set $X \subset {\bf{N}}$ such that ${\rm{card}}\left( X \right) = {\rm{min}}\left( X \right) + 1$ . The theorem we analyze is as follows. For every infinite subset M of N, for every coloring C of the exactly large subsets of M in two colors, there exists and infinite subset L of M such that C is constant on all exactly large subsets of L. This theorem is essentially due to Pudlák and Rödl and independently to Farmak

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22

Akbari, S., M. Chavooshi, M. Ghanbari, and S. Zare. "The f-Chromatic Index of a Graph Whose f-Core Has Maximum Degree 2." Canadian Mathematical Bulletin 56, no. 3 (2013): 449–58. http://dx.doi.org/10.4153/cmb-2012-046-3.

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Abstract.Let G be a graph. The minimum number of colors needed to color the edges of G is called the chromatic index of G and is denoted by χ'(G). It is well known that , for any graph G, where Δ(G) denotes the maximum degree of G. A graph G is said to be class 1 if x'(G) = Δ(G) and class 2 if χ'(G) = Δ(G)+1. Also, GΔ is the induced subgraph on all vertices of degree Δ(G). Let f : V(G) → ℕ be a function. An f-coloring of a graph G is a coloring of the edges of E(G) such that each color appears at each vertex v ∊ V(G) at most f (v) times. The minimum number of colors needed to f-color G is call

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23

Frankfurt, L., and M. Strikman. "On Hard Coherent Processes." Acta Physica Polonica B 56, no. 3 (2025): 1. https://doi.org/10.5506/aphyspolb.56.3-a23.

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A factorization theorem for the hard coherent processes involving high-energy scattering of photons is derived. We elaborate the treatment for the case of the longitudinally polarized photons and extend the treatment to the case of the processes initiated by transversely polarized photons, as well as to the coherent photo-production of heavy quarkonia. A wave function of a hadron being the solution of the Schrödinger equation is presented in the space-time evolution of initially zero-size and zero-color charge wave packet of bare quarks and gluons. The increase of the running coupling constant

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KNEISSLER, JAN A. "WOVEN BRAIDS AND THEIR CLOSURES." Journal of Knot Theory and Its Ramifications 08, no. 02 (1999): 201–14. http://dx.doi.org/10.1142/s0218216599000122.

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A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence tame links can be presented as plats and closures of woven braids. Restricting on knots we get the 'woven version' of the well-known theorem of Markov, giving moves that are capable of producing all woven braids with equivalent closures. As corollary we obtain that a link in which each component is dyed with at least two different colors can be projected on a plane without crossing strands of the same color. The lowest order part of the HO

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Kristiana, Arika Indah, Elisa Rachmasari, Dafik ., Ika Hesti Agustin, Indah Luthfiyah Mursyidah, and Ridho Alfarisi. "On b-Coloring Analysis of Graphs: An Application to Spatial-Temporal Graph Neural Networks for Multi-Step Time Series Forecasting of Soil Moisture and pH in Companion Farming." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3356–69. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5409.

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Let $G$ be a pair of two sets $(V,E)$ with vertex set $V$ and edge set $E$. A proper coloring of a graph $G$ is a vertex coloring of it such that no two adjacent vertices in $G$ have the same color. By $b-$Coloring, we define a coloring of the vertex of $G$ such that each color class has at least one vertex that adjacent with all other color classes. The $b-chromatic$ number of graph $G$, denoted by $\varphi(G),$ is the largest integer $k$ such that graph $G$ has $b-$Coloring with $k$ colors. In this paper, we will explore some new lemmas or theorems regarding to $\varphi(G)$. Furthermore, to

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Liou, Jeih-Jang. "A Novel Color Recognition Model for Improvement on Color Differences in Products via Grey Relational Grade." Axioms 10, no. 4 (2021): 266. http://dx.doi.org/10.3390/axioms10040266.

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ED light, a green energy-saving light source, can cause color cast. For this reason, LED light is seldom favored by designers. The purpose of the paper is to provide shoppers who are observing product colors in an LED-lighted setting with an innovative color identification model. Based on designers’ product color comparison, the paper employs high-reliability mechanic visual perception in combination with grey relational grade. Grey relational grade is applied to eliminate electrical fault pertaining to mechanic visual perception, whereby appropriate LED parameters and color cast inclination c

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27

Et.al, Eunchong Ha. "Color Interactive Contents System using Kinect Camera Calibration." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (2021): 786–91. http://dx.doi.org/10.17762/turcomat.v12i6.2096.

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Recently, media content that interacts in real time is increasing. In this paper, we introduce a real-time color extraction content system that utilizes the Kinect camera used in ‘COLOR’ media art. The Kinect camera used in the work detects and tracks the joints of the visitors that enter the exhibition space. Kinect detected data is mapped to color calibration in a Unity environment to generate a point cloud video. Get the pixel color of the spine shoulder joint coordinates of the visitor in the point cloud image. The color data is output on the screen in the form of color one, and passes thr

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28

Yang, Jian Hua. "Two-Tone Colored Petri Net and its Application in PLC." Applied Mechanics and Materials 404 (September 2013): 618–23. http://dx.doi.org/10.4028/www.scientific.net/amm.404.618.

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2-tone colored Petri net, where one color of tokens stands for logical value true and the other color of tokens for logical value false, is proposed to solve problem of inconsistency between programmable logic control. Symmetry 2-tone colored Petri net is also developed to keep the dynamic behavior in accordance with that of the original Petri net so that invariant method can be employed to analyze properties of nets. Some theorems are given to judge circular control based on reachable tree and T-invariants, and the algorithm for obtaining all minimal T-invariants of symmetry 2-tone colored Pe

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Patey, Ludovic, and Keita Yokoyama. "The proof-theoretic strength of Ramsey's theorem for pairs and two colors." Advances in Mathematics 330 (May 2018): 1034–70. http://dx.doi.org/10.1016/j.aim.2018.03.035.

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Espinoza, Jorge, and David Plaza. "Blob algebra and two-color Soergel calculus." Journal of Pure and Applied Algebra 223, no. 11 (2019): 4708–45. http://dx.doi.org/10.1016/j.jpaa.2019.02.013.

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Barbiere, J. Michael, Ana Vidal, and Debra A. Zellner. "The Color of Music: Correspondence through Emotion." Empirical Studies of the Arts 25, no. 2 (2007): 193–208. http://dx.doi.org/10.2190/a704-5647-5245-r47p.

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College students listened to four song clips. Following each clip, the students indicated which color(s) corresponded to each of the four songs by distributing five points among eleven basic color names. Each song had previously been identified as either a “happy” or “sad” song. Each participant listened to two “happy” and two “sad” songs in random order. There was more agreement in color choice for the songs eliciting the same emotions than for songs eliciting different emotions. Brighter colors such as yellow, red, green, and blue were usually assigned to the happy songs and gray was usually

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PLOŠČICA, MIROSLAV. "CONGRUENCE LIFTING OF SEMILATTICE DIAGRAMS." International Journal of Algebra and Computation 19, no. 07 (2009): 911–24. http://dx.doi.org/10.1142/s021819670900541x.

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We consider the problem, whether the algebras in two finitely generated congruence-distributive varieties have isomorphic congruence lattices. According to the results of P. Gillibert, this problem is closely connected with the question, which diagrams of finite distributive semilattices can be represented by the congruence lattices of algebras in a given variety. We study this question for varieties of bounded lattices, generated by different nondistributive lattices of length 2 (denoted Mn). For each pair from this family of varieties we construct a diagram indexed by the product of three fi

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Rapoport, Aviva. "Experimentally Elicited Judgments of Color Harmony." Empirical Studies of the Arts 12, no. 1 (1994): 63–83. http://dx.doi.org/10.2190/9gf8-0ttn-brp8-qlx5.

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Eight variants of each of four different geometrical forms were constructed by varying the proportions of six different colors. All possible pairs of the resulting colored pictures were presented to subjects who were asked to determine 1) which of the two pictures is more harmonious, and 2) by how much one picture is more harmonious than the other. Scaling of both individual and group data shows that subjects can produce consistent judgments of harmony which are measurable by a ratio scale. Two models of color harmony based on the work of Munsell and Itten yield similar predictions of color pr

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Maraston, Claudia. "A Modular Tool for the Evolutionary Synthesis of Stellar Populations." Symposium - International Astronomical Union 171 (1996): 409. http://dx.doi.org/10.1017/s0074180900233287.

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An innovative tool for the construction of Evolutionary Synthesis models of Stellar Populations is presented. It is based on three independent matrices giving respectively 1) the fuel consumption during each evolutionary phase as a function of stellar mass, 2) the typical temperatures and gravities during such phases, and 3) colors and bolometric corrections as a function of gravity and temperature. The first matrix allows to calculate the relative contribution of each phase to the bolometric light of the population, thanks to the so-called Fuel Consumption Theorem (Renzini & Buzzoni 1986,

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35

Durbin, B. P., and D. M. Rocke. "Variance-stabilizing transformations for two-color microarrays." Bioinformatics 20, no. 5 (2004): 660–67. http://dx.doi.org/10.1093/bioinformatics/btg464.

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36

Salop, Steven C. "Evaluating Uncertain Evidence With Sir Thomas Bayes: A Note For Teachers." Journal of Economic Perspectives 1, no. 1 (1987): 155–60. http://dx.doi.org/10.1257/jep.1.1.155.

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Consider the following problem: On the night of March 1, 1986, in Lorain, Ohio, John Doe was struck by a speeding taxi as he crossed the street. The taxi was driving the wrong way down a one-way street and did not stop. An eyewitness thought that the taxi was blue. Doe has sued the Blue Cab Company for his medical expenses in a tort claim. Lorain has only two taxi companies, Blue Cab and Green Cab. Green Cab is the dominant firm with 85 percent of the taxis registered in the town. According to uncontroverted evidence, the eyewitness was 80 percent reliable in identifying the color of taxis; th

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Diemunsch, Jennifer, Michael Ferrara, Sogol Jahanbekam, and James M. Shook. "Extremal Theorems for Degree Sequence Packing and the Two-Color Discrete Tomography Problem." SIAM Journal on Discrete Mathematics 29, no. 4 (2015): 2088–99. http://dx.doi.org/10.1137/140987912.

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Stewart, Ian. "Finite Characterization of the Coarsest Balanced Coloring of a Network." International Journal of Bifurcation and Chaos 30, no. 14 (2020): 2050212. http://dx.doi.org/10.1142/s0218127420502120.

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Balanced colorings of networks correspond to flow-invariant synchrony spaces. It is known that the coarsest balanced coloring is equivalent to nodes having isomorphic infinite input trees, but this condition is not algorithmic. We provide an algorithmic characterization: two nodes have the same color for the coarsest balanced coloring if and only if their [Formula: see text]th input trees are isomorphic, where [Formula: see text] is the number of nodes. Here [Formula: see text] is the best possible. The proof is analogous to that of Leighton’s theorem in graph theory, using the universal cover

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Chaudhury, Ranjan, Debashis Gangopadhyay, and Samir K. Paul. "Van Der Waerden's Coloring Theorem and Classical Spin Systems." Modern Physics Letters B 11, no. 21n22 (1997): 923–28. http://dx.doi.org/10.1142/s0217984997001134.

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We find a non-invertible matrix representation for Van der Waerden's coloring theorem for two distinct colors in a one-dimensional periodic lattice. Using this, an infinite one-dimensional antiferromagnetic Ising system is mapped to a pseudo-ferromagnetic one, thereby relating the couplings. All this is reminiscent of renormalization group.

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Gabeleh, Moosa. "Common best proximity pairs in strictly convex Banach spaces." Georgian Mathematical Journal 24, no. 3 (2017): 363–72. http://dx.doi.org/10.1515/gmj-2016-0021.

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AbstractA mapping {T\colon A\cup B\to A\cup B} such that {T(A)\subseteq A} and {T(B)\subseteq B} is called a noncyclic mapping, where A and B are two nonempty subsets of a Banach space X. A best proximity pair {(p,q)\in A\times B} for such a mapping T is a point such that {p=Tp,q=Tq} and {\|p-q\|=\operatorname{dist}(A,B)}. In the current paper, we establish some existence results of best proximity pairs in strictly convex Banach spaces. The presented theorems improve and extend some recent results in the literature. We also obtain a generalized version of Markov–Kakutani’s theorem for best pro

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Yahya, Nisky Imansyah, Ainun Fatmawati, Nurwan Nurwan, and Salmun K. Nasib. "RAINBOW VERTEX-CONNECTION NUMBER ON COMB PRODUCT OPERATION OF CYCLE GRAPH (C_4) AND COMPLETE BIPARTITE GRAPH (K_(3,N))." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 2 (2023): 0673–84. http://dx.doi.org/10.30598/barekengvol17iss2pp0673-0684.

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Rainbow vertex-connection number is the minimum colors assignment to the vertices of the graph, such that each vertex is connected by a path whose edges have distinct colors and is denoted by . The rainbow vertex connection number can be applied to graphs resulting from operations. One of the methods to create a new graph is to perform operations between two graphs. Thus, this research uses comb product operation to determine rainbow-vertex connection number resulting from comb product operation of cycle graph and complete bipartite graph & . The research finding obtains the theorem of rai

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Lee, Sungho. "Interrogating the Color Line: A Critique of Two-Race Culture and the Possibility of an Inclusive Blackness in “The Wife of His Youth”." Criticism and Theory Society of Korea 28, no. 3 (2023): 217–43. http://dx.doi.org/10.19116/theory.2023.28.3.217.

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Charles Chesnutt’s works have been extensively studied for their exploration of cultural and racial hybridity, as they demonstrate a radical impulse to reject the postbellum American notion of a Manichaean racial divide. Chesnutt’s discussion of the black question revolves around cross-fertilization and inner conflicts that stem from cultural, racial amalgamation. In challenging the notion of race as a cultural construct, Chesnutt opposes two-race politics, envisioning a racial landscape that goes beyond both cultural assimilation and ethnic enclave-building. This paper explores Chesnutt

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Saluja, G. S. "Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space." Tamkang Journal of Mathematics 38, no. 1 (2007): 85–92. http://dx.doi.org/10.5556/j.tkjm.38.2007.96.

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In this paper, we study strong convergence of common fixed points of two asymptotically quasi-nonexpansive mappings and prove that if $K$ is a nonempty closed convex subset of a real Banach space $E$ and let $ S, T\colon K\to K $ be two asymptotically quasi-nonexpansive mappings with sequences $ \{u_n\}$, $\{v_n\}\subset [0,\infty) $ such that $ \sum_{n=1}^{\infty}u_n

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Bildhauer, Michael, and Martin Fuchs. "Liouville-type results in two dimensions for stationary points of functionals with linear growth." Annales Fennici Mathematici 47, no. 1 (2022): 417–26. http://dx.doi.org/10.54330/afm.114681.

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We consider elliptic systems generated by variational integrals of linear growth satisfying the condition of \(\mu\)-ellipticity for some exponent \(\mu >1\) and prove that stationary points \(u\colon\mathbb{R}^2\to\mathbb{R}^N\) with the property \(\limsup_{|x|\to \infty} \frac{|u(x)|}{|x|} < \infty\) must be affine functions. The latter condition can be dropped in the scalar case together with appropriate assumptions on the energy density providing an extension of Bernstein's theorem.

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Karra.NAGA, SIVA SURYA DILEEP, SAI SRI RAMA RAJU Krovvidi.KARTHIK, Karella.JOHNY, Kombathula.VENKAT, and VASA RAO P.SRINU. "E-Mail Spam Detection Using Machine Learning Naive Bayes Theorem." International Journal of Innovative Science and Research Technology (IJISRT) 9, no. 2 (2024): 5. https://doi.org/10.5281/zenodo.10725536.

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Spam, sometimes called spam, is unsolicited email that is typically sent to large lists of recipients. Although real individuals can send spam, botnets (computer networks infected by an attacker known as a "bully") are often responsible for sending spam. While most people view spam as a problem, they believe it is a result of email communication. In addition to being annoying, spam can also be dangerous because it can clog email inboxes if not filtered properly and deleted frequently. Spammers or spammers often change their methods and content to trick victims into downloading malware, sharing

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Sotskov, Yuri N., and Evangelina I. Mihova. "Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem." Algorithms 14, no. 8 (2021): 246. http://dx.doi.org/10.3390/a14080246.

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This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness Lmax for integer due dates to the scheduling problem, where along with precedence constraints given on the set V={v1,v2, …,vn} of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set V. We prove that the extended scheduling problem with integer release times ri≥0 of th

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DAS, SANDIP, PARTHA P. GOSWAMI, and SUBHAS C. NANDY. "SMALLEST COLOR-SPANNING OBJECT REVISITED." International Journal of Computational Geometry & Applications 19, no. 05 (2009): 457–78. http://dx.doi.org/10.1142/s0218195909003076.

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Given a set of n colored points in IR2 with a total of m (3 ≤ m ≤ n) colors, the problem of identifying the smallest color-spanning object of some predefined shape is studied in this paper. We shall consider two different shapes: (i) corridor and (ii) rectangle of arbitrary orientation. Our proposed algorithm for identifying the smallest color-spanning corridor is simple and runs in O(n2 log n) time using O(n) space. A dynamic version of the problem is also studied, where new points may be added, and the narrowest color-spanning corridor at any instance can be reported in O(mn(α(n))2 log m) ti

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Sunder, R., Ika Hesti Agustin, Dafik Dafik, Ika Nur Maylisa, N. Mohanapriya, and Marsidi Marsidi. "On Local Antimagic b-Coloring and Its Application for STGNN Time Series Forecasting on Horizontal Farming." CAUCHY: Jurnal Matematika Murni dan Aplikasi 10, no. 1 (2025): 117–32. https://doi.org/10.18860/cauchy.v10i1.29968.

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This article discusses a local antimagic coloring which is a combination between antimagic labeling and coloring. It is a new notion. We define a vertex weight of as where is the set of edges incident to . The bijection is said to be a local antimagic labeling if for any two adjacent vertices, their vertex weights must be distinct. Furthermore a coloring of a graph is a proper coloring of the vertices of such that in each color class there exists a vertex having neighbors in all other color classes. If we assign color on each vertex by the vertex weight such that it induces a graph coloring sa

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Ballantine, Cristina, and Mircea Merca. "Combinatorial proof of the minimal excludant theorem." International Journal of Number Theory 17, no. 08 (2021): 1765–79. http://dx.doi.org/10.1142/s1793042121500615.

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The minimal excludant of a partition [Formula: see text], [Formula: see text], is the smallest positive integer that is not a part of [Formula: see text]. For a positive integer [Formula: see text], [Formula: see text] denotes the sum of the minimal excludants of all partitions of [Formula: see text]. Recently, Andrews and Newman obtained a new combinatorial interpretation for [Formula: see text]. They showed, using generating functions, that [Formula: see text] equals the number of partitions of [Formula: see text] into distinct parts using two colors. In this paper, we provide a purely combi

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Yang, Chu-Wen, Chin-Fu Hsiao, and Chen-Kung Chou. "Evaluation of Experimental Designs for Two-Color cDNA Microarrays." Journal of Computational Biology 12, no. 9 (2005): 1202–20. http://dx.doi.org/10.1089/cmb.2005.12.1202.

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