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Relevant bibliographies by topics / Proper coloring

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Journal articles

Academic literature on the topic 'Proper coloring'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Proper coloring"

1

Ma, Baolin, and Chao Yang. "Distinguishing colorings of graphs and their subgraphs." AIMS Mathematics 8, no. 11 (2023): 26561–73. http://dx.doi.org/10.3934/math.20231357.

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<abstract><p>In this paper, several distinguishing colorings of graphs are studied, such as vertex distinguishing proper edge coloring, adjacent vertex distinguishing proper edge coloring, vertex distinguishing proper total coloring, adjacent vertex distinguishing proper total coloring. Finally, some related chromatic numbers are determined, especially the comparison of the correlation chromatic numbers between the original graph and the subgraphs are obtained.</p></abstract>

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2

Goddard, Wayne, and Robert Melville. "Coloring subgraphs with restricted amounts of hues." Open Mathematics 15, no. 1 (2017): 1171–80. http://dx.doi.org/10.1515/math-2017-0098.

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Abstract We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we consider (not necessarily proper) colorings of the vertices of a graph G such that, for every copy of F in G, the number of colors it receives is in A. This generalizes proper colorings, defective coloring, and no-rainbow coloring, inter alia. In this paper we focus on the case that A is a singleton set. In particular, we investigate the colorings where the graph F is a star or is 1-regular.

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3

Chartrand, Gary, James Hallas, and Ping Zhang. "Royal Colorings of Graphs." Ars Combinatoria 156 (July 31, 2023): 51–63. http://dx.doi.org/10.61091/ars156-06.

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For a graph \(G\) and a positive integer \(k\), a royal \(k\)-edge coloring of \(G\) is an assignment of nonempty subsets of the set \(\{1, 2, \ldots, k\}\) to the edges of \(G\) that gives rise to a proper vertex coloring in which the color assigned to each vertex \(v\) is the union of the sets of colors of the edges incident with \(v\). If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal \(k\)-coloring. The minimum positive integer \(k\) for which a graph has a strong royal \(k\)-coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.

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Chartrand, Gary, James Hallas, and Ping Zhang. "Royal Colorings of Graphs." Ars Combinatoria 156 (July 31, 2023): 51–63. http://dx.doi.org/10.61091/ars156-6.

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For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v . If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal k coloring. The minimum positive integer k for which a graph has a strong royal k -coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.

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5

Keszegh, Balázs, and Dömötör Pálvölgyi. "Proper Coloring of Geometric Hypergraphs." Discrete & Computational Geometry 62, no. 3 (2019): 674–89. http://dx.doi.org/10.1007/s00454-019-00096-9.

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6

Bagheri Gh., Behrooz, and Behnaz Omoomi. "On the simultaneous edge coloring of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (2014): 1450049. http://dx.doi.org/10.1142/s1793830914500499.

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A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et al. (2000) conjectured that every bridgeless bipartite graph is 2-simultaneous edge colorable. Luo et al. (2004) showed that every bipartite graphic sequence S with all its elements greater than one, has a realization that admits a 2-simultaneous edge coloring. In this paper, the μ-simultaneous edge coloring of graphs is studied. Moreover, the properties of the extremal counterexample to the above conjecture are investigated. Also, a relation between 2-simultaneous edge coloring of a graph and a cycle double cover with certain properties is shown and using this relation, some results about 2-simultaneous edge colorable graphs are obtained.

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7

Zhou, Yangyang, Dongyang Zhao, Mingyuan Ma, and Jin Xu. "Domination Coloring of Graphs." Mathematics 10, no. 6 (2022): 998. http://dx.doi.org/10.3390/math10060998.

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A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by χdd(G). In this paper, we study the complexity of the k-domination coloring problem by proving its NP-completeness for arbitrary graphs. We give basic results and properties of χdd(G), including the bounds and characterization results, and further research χdd(G) of some special classes of graphs, such as the split graphs, the generalized Petersen graphs, corona products, and edge corona products. Several results on graphs with χdd(G)=χ(G) are presented. Moreover, an application of domination colorings in social networks is proposed.

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8

Li, Minhui, Shumin Zhang, Caiyun Wang, and Chengfu Ye. "The Dominator Edge Coloring of Graphs." Mathematical Problems in Engineering 2021 (October 7, 2021): 1–7. http://dx.doi.org/10.1155/2021/8178992.

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Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .

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9

Kristiana, Arika Indah, Ahmad Aji, Edy Wihardjo, and Deddy Setiawan. "on Graceful Chromatic Number of Vertex amalgamation of Tree Graph Family." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 3 (2022): 432–44. http://dx.doi.org/10.18860/ca.v7i3.16334.

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Proper vertex coloring c of a graph G is a graceful coloring if c is a graceful k-coloring for k∈{1,2,3,…}. Definition graceful k-coloring of a graph G=(V,E) is a proper vertex coloring c:V(G)→{1,2,…,k);k≥2, which induces a proper edge coloring c':E(G)→{1,2,…,k-1} defined c'(uv)=|c(u)-c(v)|. The minimum vertex coloring from graph G can be colored with graceful coloring called a graceful chromatic number with notation χg (G). In this paper, we will investigate the graceful chromatic number of vertex amalgamation of tree graph family with some graph is path graph, centipede graph, broom and E graph.

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10

Sagan, Bruce, and Vincent Vatter. "Bijective Proofs of Proper Coloring Theorems." American Mathematical Monthly 128, no. 6 (2021): 483–99. http://dx.doi.org/10.1080/00029890.2021.1901460.

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