Rainbow Cycles in Bipartite Graphs

Let $G = (V, E)$ be a graph on $n$ vertices, and let $c : E \to P$, where $P$ is a set of colors. Let $\delta^c(G) = \min_{v \in V} \{ d^{c}(v) \}$ where $d^c(v)$ is the number of colors on edges incident to a vertex $v$ of $G$. We show sufficient conditions on $\delta^c(G)$ for the existence of a rainbow cycle of length $2k$ in sufficiently large bipartite graphs $G$. In many cases, we also show the condition to be tight. This is joint work with Andrzej Czygrinow.