Rainbow cycles in edge-colored graphs

Let G be a graph of order n with an edge coloring c, and let δc(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least δc(G) edges having pairwise distinct colors. A subgraph F⊂G is rainbow if all edges of F have pairwise distinct colo...

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Bibliographic Details
Published inDiscrete mathematics Vol. 339; no. 4; pp. 1387 - 1392
Main Authors Čada, Roman, Kaneko, Atsushi, Ryjáček, Zdeněk, Yoshimoto, Kiyoshi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.04.2016
Subjects
Color
Color degree condition
Coloring
Edge coloring
Graph theory
Graphs
Integers
Mathematical analysis
Rainbow coloring
Rainbow cycle
Rainbows
Color degree condition
Rainbow cycle
Rainbow coloring
Edge coloring
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Summary:Let G be a graph of order n with an edge coloring c, and let δc(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least δc(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 δc(G)>n3+1, then G contains a rainbow C4, and (ii) if δc(G)>n2+2, then G contains a rainbow cycle of length at least 4.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2015.12.003