Find out an algorithm that finds out if an undirected graph contains even length cycle or not using BFS?
Construct a new graph $G'$ with the same set of vertices, and with an edge $(u,v)$ iff there is a path of length 2 from $u$ to $v$ in the original graph.  Then, check whether $G'$ has any cycles of any length.  A cycle in $G'$ corresponds to an even-length cycle in the original graph, and vice versa, so this provides a correct algorithm.  The running time is $O(|V||E|)$.