Color degree and alternating cycles in edge-colored graphs

Let GG be an edge-colored graph. An alternating cycle of GG is a cycle of GG in which any two consecutive edges have distinct colors. Let dc(v)dc(v), the color degree of a vertex vv, be defined as the maximum number of edges incident with vv that have distinct colors. In this paper, we study color degree conditions for the existence of alternating cycles of prescribed length.