Results 21 to 30 of about 9,612,020 (345)
Subgraphs of large connectivity and chromatic number [PDF]
Bulletin of the London Mathematical Society, 2020 Resolving a problem raised by Norin in 2020, we show that for each k∈N$k \in \mathbb {N}$ , the minimal f(k)∈N$f(k) \in \mathbb {N}$ with the property that every graph G$G$ with chromatic number at least f(k)+1$f(k)+1$ contains a subgraph H$H$ with both ...
António Girão, Bhargav P. Narayanan
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Hasse diagrams with large chromatic number [PDF]
Bulletin of the London Mathematical Society, 2020 For every positive integer n , we construct a Hasse diagram with n vertices and independence number O(n3/4) . Such graphs have chromatic number Ω(n1/4) , which significantly improves the previously best‐known constructions of Hasse diagrams having ...
Andrew Suk, István Tomon
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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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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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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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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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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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Advances in Mathematics, 1999 From the article: We consider graphs \({\mathcal G}=(X,R)\) where the vertex set \(X\) is a standard Borel space (i.e., a complete separable metrizable space equipped with its \(\sigma\)-algebra of Borel sets), and the edge relation \(R\subseteq X^2\) is ``definable,'' i.e., Borel, analytic, coanalytic, etc.
Kechris, A. S. +2 more
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