@article{88783348a59b4726993941ef70858c50,
title = "Finding a Shortest Odd Hole",
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.",
keywords = "Induced subgraph, recognition algorithm, shortest odd hole",
author = "Maria Chudnovsky and Alex Scott and Paul Seymour",
note = "Funding Information: This material is based upon work supported in part by the U. S. Army Research Office under grant number W911NF-16-1-0404. The first author was supported by NSF grant DMS 1763817. The third author was supported by AFOSR grant A9550-19-1-0187, and NSF grant DMS-1800053. Authors{\textquoteright} addresses: M. Chudnovsky and P. Seymour, Princeton University, Princeton, NJ, 08544; emails: {mcudnov, pds}@math.princeton.edu; A. Scott, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK; email: scott@maths.ox.ac.uk. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. {\textcopyright} 2021 Association for Computing Machinery. 1549-6325/2021/04-ART13 $15.00 https://doi.org/10.1145/3447869 Publisher Copyright: {\textcopyright} 2021 ACM.",
year = "2021",
month = jun,
doi = "10.1145/3447869",
language = "English (US)",
volume = "17",
journal = "ACM Transactions on Algorithms",
issn = "1549-6325",
publisher = "Association for Computing Machinery (ACM)",
number = "2",
}