Rainbow cliques in edge-colored graphs
نویسندگان
چکیده
منابع مشابه
Large Rainbow Matchings in Edge-Colored Graphs
A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident with v. Wang and Li conjectured that for k ≥ 4, every edge-colored graph with minimum color degree k contains a rainbow matching of size at least dk/2e. A properly edge-colored K4 has no such matching, which motivates the ...
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Let G be a properly edge colored graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree of G. We show that if |V (G)| ≥ 8δ 5 , then G has a rainbow matching of size at least ⌊ 5 ⌋. We also prove that if G is a properly colored triangle-free graph, then G has a rainbow matching of size at least ⌊ 3 ⌋.
متن کاملRainbow Matching in Edge-Colored Graphs
A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident to v. Wang and Li conjectured that for k > 4, every edge-colored graph with minimum color degree at least k contains a rainbow matching of size at least ⌈k/2⌉. We prove the slightly weaker statement that a rainbow matching...
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Let G be a graph of order n with an edge coloring c, and let δ(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least δ(G) edges having pairwise distinct colors. A subgraph F ⊂ G is rainbow if all edges of F have pairwise distinct colors. In this paper, we prove that (i) if G is triangle-free and δ(G) > n3 + 1, then G contains a r...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2016
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2015.12.013