Smallest odd holes in claw-free graphs (extended abstract)

Shimon Shrem, Michal Stern, Martin Charles Golumbic

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper, we give general structure properties of a smallest odd hole in a claw-free graph that lead to a polynomial time algorithm. The algorithm is based on a modified BFS we call Γ-BFS. For a graph G with n vertices and m edges, the time complexity of the algorithm is O(nm 2). The algorithm is very easy to implement. We conclude the paper with a suggestion for an extension of our approach in order to detect an odd hole in a general graph.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 35th International Workshop, WG 2009, Revised Papers
Number of pages12
StatePublished - 2010
Event35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009 - Montpellier, France
Duration: 24 Jun 200926 Jun 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5911 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009


  • Claw-free graphs
  • Holes
  • Odd holes
  • Polynomial time algorithms
  • Triangle-free graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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