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Tree‐Chromatic Number Is Not Equal to Path‐Chromatic Number* [PDF]
Journal of Graph Theory, 2017 AbstractFor a graph G and a tree‐decomposition of G, the chromatic number of is the maximum of , taken over all bags . The tree‐chromatic number of G is the minimum chromatic number of all tree‐decompositions of G. The path‐chromatic number of G is defined analogously.
Huynh T., Kim R.
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DICHROMATIC NUMBER AND FRACTIONAL CHROMATIC NUMBER [PDF]
Forum of Mathematics, Sigma, 2016 The dichromatic number of a graph $G$ is the maximum integer $k$
BOJAN MOHAR, HEHUI WU
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The open monophonic chromatic number of a graph [PDF]
Journal of Hyperstructures, 2023 A set P of vertices in a connected graph G is called open monophonic chromatic set if P is both an open monophonic set and a chromatic set. The minimum cardinality among the set of all open monophonic chromatic sets is called open monophonic chromatic ...
Mohammed Abdul Khayyoom +1 more
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Separating tree-chromatic number from path-chromatic number [PDF]
Journal of Combinatorial Theory, Series B, 2019 We apply Ramsey theoretic tools to show that there is a family of graphs which have tree-chromatic number at most~$2$ while the path-chromatic number is unbounded. This resolves a problem posed by Seymour.
Fidel Barrera-Cruz +6 more
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Local chromatic number and topology [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The local chromatic number of a graph, introduced by Erdős et al., is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph.
Gábor Simonyi, Gábor Tardos
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The game chromatic number of trees and forests [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then
Charles Dunn +4 more
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Chromatic Vertex Folkman Numbers [PDF]
The Electronic Journal of Combinatorics, 2020 For graph $G$ and integers $a_1 \ge \cdots \ge a_r \ge 2$, we write $G \rightarrow (a_1 ,\cdots ,a_r)^v$ if and only if for every $r$-coloring of the vertex set $V(G)$ there exists a monochromatic $K_{a_i}$ in $G$ for some color $i \in \{1, \cdots, r\}$.
Xu, Xiaodong +2 more
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Dynamic Chromatic Number of Bipartite Graphs [PDF]
Scientific Annals of Computer Science, 2016 A dynamic coloring of a graph G is a proper vertex coloring such that for every vertex v Î V(G) of degree at least 2, the neighbors of v receive at least 2 colors.
S. Saqaeeyan, E. Mollaahamdi
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Game Chromatic Number of Shackle Graphs
JTAM (Jurnal Teori dan Aplikasi Matematika), 2021 Coloring vertices on graph is one of the topics of discrete mathematics that are still developing until now. Exploration Coloring vertices develops in the form of a game known as a coloring game. Let G graph.
Firmansyah Firmansyah, Abdul Mujib
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The -distance chromatic number of trees and cycles
AKCE International Journal of Graphs and Combinatorics, 2019 For any positive integer , a -distance coloring of a graph is a vertex coloring of in which no two vertices at distance less than or equal to receive the same color.
Niranjan P.K., Srinivasa Rao Kola
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