Color degree and heterochromatic cycles in edge-colored graphs

Given a graph G and an edge-coloring C of G , a heterochromatic cycle of G is a cycle in which any pair of edges have distinct colors. Let d c ( v ) , named the color degree of a vertex v , be defined as the maximum number of edges incident with v that have distinct colors. In this paper, some color degree conditions for the existence of heterochromatic cycles are obtained.