Results 11 to 20 of about 27,939 (295)
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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On the chromatic number of circulant graphs
Discrete Mathematics, 2009 Given a set D of a cyclic group C, we study the chromatic number of the circulant graph G(C,D) whose vertex set is C, and there is an edge ij whenever i−j∈D∪−D.
Oriol Serra
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The Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2006 In this paper we define and study the distinguishing chromatic number, $\chi_D(G)$, of a graph $G$, building on the work of Albertson and Collins who studied the distinguishing number. We find $\chi_D(G)$ for various families of graphs and characterize those graphs with $\chi_D(G)$ $ = |V(G)|$, and those trees with the maximum chromatic distingushing ...
Karen L. Collins, Ann N. Trenk
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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-Choosability of Hypergraphs with High Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2019 It was conjectured by Ohba and confirmed by Noel, Reed and Wu that, for any graph $G$, if $|V(G)|\le 2\chi(G)+1$ then $G$ is chromatic-choosable; i.e., it satisfies $\chi_l(G)=\chi(G)$. This indicates that the graphs with high chromatic number are chromatic-choosable. We observe that this is also the case for uniform hypergraphs and further propose a
Wei Wang 0052, Jianguo Qian
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Distance graphs with maximum chromatic number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $D$ be a finite set of integers. The distance graph $G(D)$ has the set of integers as vertices and two vertices at distance $d ∈D$ are adjacent in $G(D)$.
Javier Barajas, Oriol Serra
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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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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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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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On the dominated chromatic number of certain graphs [PDF]
Transactions on Combinatorics, 2020 Let $G$ be a simple graph. The dominated coloring of $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex.
Saeid Alikhani, Mohammad Reza Piri
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