Detecting a Long Odd Hole

Abstract

For each integer ≥ 5, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least and odd.

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Acknowledgement

We would like to thank Hou Teng Cheong, who found a significant error in an earlier version of this paper.

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Correspondence to Paul Seymour.

Additional information

This material is based upon work supported in part by the U. S. Army Research Office under grant number W911NF-16-1-0404, and by NSF grant DMS-1763817.

Supported by a Leverhulme Trust Research Fellowship.

Supported by NSF grant DMS-1800053 and AFOSR grant A9550-19-1-0187, and partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach.

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Chudnovsky, M., Scott, A. & Seymour, P. Detecting a Long Odd Hole. Combinatorica 41, 1–30 (2021). https://doi.org/10.1007/s00493-020-4301-z

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Mathematics Subject Classification (2010)

  • 05C38
  • 05C85