Finding a Shortest Odd Hole

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3 Scopus citations


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.

Original languageEnglish (US)
Article number3447869
JournalACM Transactions on Algorithms
Issue number2
StatePublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


  • Induced subgraph
  • recognition algorithm
  • shortest odd hole


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