Rainbow cycles in bipartite and triangle-free graphs

H. Li proved that if an n-vertex graph G is edge-colored so that every vertex is incident to at least (n+1)/2 colors, then G contains a rainbow triangle. Subsequently, Czygrinow, Molla, Nagle, and Oursler gave an analogous condition for a general graph to have a rainbow cycle of length four. In this presentation, we will discuss rainbow cycles in edge-colored bipartite graphs and triangle-free graphs. This research is a collaborative work with X. Yuan and S. Parvatikar.