Finding a Shortest Odd Hole-Reference-Cited by-同舟云学术

Finding a Shortest Odd Hole

Published:2021-06 Issue:2 Volume:17 Page:1-21
ISSN:1549-6325
Container-title:ACM Transactions on Algorithms
language:en
Short-container-title:ACM Trans. Algorithms

Author:

Chudnovsky Maria¹,Scott Alex²,Seymour Paul³

Affiliation:

1. Princeton University, Edgbaston, Birmingham, USA

2. Mathematical Institute, University of Oxford, UK

3. Princeton University, Berkeley, CA, USA

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.

Funder

NSF

AFOSR

U. S. Army Research Office

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

Link

https://dl.acm.org/doi/pdf/10.1145/3447869

Reference9 articles.

1. Färbung von Graphen, deren sämtliche bzw. deren ungerade Kreise starr sind;Berge Claude;Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe,1961

2. On the complexity of testing for odd holes and induced odd paths

3. Corrigendum

4. Recognizing Berge Graphs

5. The strong perfect graph theorem

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