title: graph algorithm to detect even cycles
body: <p>I have an undirected graph. One edge in that graph is special. I want to find all other edges that are part of a even cycle containing the first edge.</p>
  
  <p>I don't need to enumerate all the cycles, that would be inherently NP I think. I just need to know, for each each edge, whether it satisfies the conditions above.</p>
  
  <p>A brute force search works of course but is too slow, and I'm struggling to come up with anything better. Any help appreciated.</p>