Rainbow cycles in edge-colored graphs

Let G be a graph of order n with an edge coloring c, and let delta(c)(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least delta(c)(G) edges having pairwise distinct colors. A subgraph F subset of 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 delta(c)(G) > n/3 + 1, then G contains a rainbow C-4, and (ii) if delta(c)(G) > n/2 + 2, then G contains a rainbow cycle of length at least 4. (C) 2015 Elsevier B.V. All rights reserved.