Why is there no literature on finding odd holes in a general undirected graph? I found this paper that seems to enumerate ALL chordless cycles (http://arxiv.org/pdf/1309.1051v4.pdf) but apparently, I read somewhere else that finding odd holes in the graph is a more difficult problem (and possibly open?)
Why can't we pull out the odd holes from the cycles found above? Furthermore, is it possible to find just ONE odd hole in a graph efficiently?
It is possible to find an even-hole in time $O(n^{11})$.
But strangely for finding an odd-hole, we don't know if there's a polynomial-time algorithm that does so. And we don't know if it's NP-Hard.
This is based on the following reference : https://arxiv.org/abs/1311.0358.
You can check the related work section.