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.

中文翻译：

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寻找最短的奇数洞

图中的奇数洞是奇数长度大于 3 的诱导循环。在较早的论文（与 Sophie Spirkl 合作）中，解决了一个长期存在的开放问题，我们给出了一个多项式时间算法来测试图是否有奇数洞。我们随后表明，对于每个吨, 有一个多项式时间算法来测试一个图是否至少包含一个长度为奇数的洞吨. 在这篇文章中，我们给出了一个算法来找到一个最短的奇洞（如果存在的话）。