I'd be grateful for some pointers to get me started on this.

We have an undirected simple graph $G = (V, E)$. Each edge is colored either blue or red.

I am interested in simple cycles (no repeated vertices or edges other than the starting and ending vertices) that have exactly one blue edge (and the rest of the edges red). Specifically, I want to enumerate these types of cycles in increasing order of length. Do there exist efficient algorithms for this task, or is there a simple reduction to a known problem? What if we restrict $G$ to be planar?

Thanks in advance.