Note on rainbow cycles in edge-colored graphs |
| |
Institution: | Center for Combinatorics and LPMC Nankai University, Tianjin 300071, China |
| |
Abstract: | Let G be a graph of order n with an edge-coloring c, and let denote the minimum color-degree of G. A subgraph F of G is called rainbow if all edges of F have pairwise distinct colors. There have been a lot of results on rainbow cycles of edge-colored graphs. In this paper, we show that (i) if , then every vertex of G is contained in a rainbow triangle; (ii) if and , then every vertex of G is contained in a rainbow ; (iii) if G is complete, and , then G contains a rainbow cycle of length at least k, where . |
| |
Keywords: | Edge-coloring Edge-colored graph Rainbow cycle Color-degree condition |
本文献已被 ScienceDirect 等数据库收录! |
|