Abstract
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.
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