寻找最短的奇洞

ACM Transactions on Algorithms (TALG) Pub Date : 2020-04-24 DOI:10.1145/3447869

M. Chudnovsky, A. Scott, P. Seymour

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引用次数: 6

摘要

图中的奇孔是奇长度大于3的诱导循环。在之前的一篇论文中(与Sophie Spirkl合作)，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一个图是否有一个奇洞。我们随后证明，对于每一个t，存在一个多项式时间算法来测试一个图是否包含长度至少为t的奇洞。在本文中，我们给出了一个算法，如果存在一个最短的奇洞，则找到一个最短的奇洞。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Finding a Shortest Odd Hole

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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ACM Transactions on Algorithms (TALG)

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