Abstract
An odd hole in a graph is an induced cycle with odd length greater than 3. In an earlier paper (with Sophie Spirkl), solving a longstanding open problem, we gave a polynomial-time algorithm to test if a graph has an odd hole. We subsequently showed that, for every t , there is a polynomial-time algorithm to test whether a graph contains an odd hole of length at least t . In this article, we give an algorithm that finds a shortest odd hole, if one exists.
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