Results 11 to 20 of about 9,612,020 (345)
The b-Chromatic Number of Star Graph Families
Le Matematiche, 2010 In this paper, we investigate the b-chromatic number of central graph, middle graph and total graph of star graph, denoted by C(K1,n), M(K1,n) and T(K1,n) respectively.
Vivin J. Vernold, M. Venkatachalam
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Game chromatic number of lexicographic product graphs
AKCE International Journal of Graphs and Combinatorics, 2015 In this paper, we determine the exact values of the game chromatic number of lexicographic product of path P2 with path Pn, star K1,n and wheel Wn. Also we give an upper bound for the game chromatic number of lexicographic product of any two simple ...
R. Alagammai, V. Vijayalakshmi
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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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New eigenvalue bound for the fractional chromatic number [PDF]
Journal of Graph Theory, 2022 Given a graph G $G$ , we let s+(G) ${s}^{+}(G)$ denote the sum of the squares of the positive eigenvalues of the adjacency matrix of G $G$ , and we similarly define s−(G) ${s}^{-}(G)$ . We prove that χf(G)≥1+maxs+(G)s−(G),s−(G)s+(G) ${\chi }_{f}(G)\ge 1+\
Krystal Guo, Sam Spiro
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Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree [PDF]
Journal of Graph Theory, 2021 Let H H be a tree. It was proved by Rödl that graphs that do not contain H H as an induced subgraph, and do not contain the complete bipartite graph Kt , t Kt,t as a subgraph, have bounded chromatic number.
A. Scott, P. Seymour, S. Spirkl
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The Odd Chromatic Number of a Planar Graph is at Most 8 [PDF]
Graphs and Combinatorics, 2022 Petruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex $$x \in V(G)$$ x ∈ V ( G ) there exists a colour c appearing an odd number ...
J. Petr, Julien Portier
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The chromatic number of heptagraphs [PDF]
Journal of Graph Theory, 2022 A pentagraph is a graph without cycles of length 3 or 4 and without induced cycles of odd length at least 7, and a heptagraph is one without cycles of length less than 7 and without induced cycles of odd length at least 9.
Di Wu, Baogang Xu, Yian Xu
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Circular Chromatic Number of Signed Graphs [PDF]
Electronic Journal of Combinatorics, 2020 A signed graph is a pair $(G, \sigma)$, where $G$ is a graph (loops and multi edges allowed) and $\sigma: E(G) \to \{+, -\}$ is a signature which assigns to each edge of $G$ a sign. Various notions of coloring of signed graphs have been studied.
R. Naserasr +2 more
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Box and Segment Intersection Graphs with Large Girth and Chromatic Number [PDF]
Advances in Combinatorics, 2020 We prove that there are intersection graphs of axis-aligned boxes in R3 and intersection graphs of straight lines in R3 that have arbitrarily large girth and chromatic number.
James Davies
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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
openaire +3 more sources