Smallest Odd Holes in Claw-Free Graphs (Extended Abstract)

Authors:
Shimon Shrem;Michal Stern;Martin Charles Golumbic
Affiliations:
Caesarea Rothschild Institute and Department of Computer Science, University of Haifa,;The Academic College of Tel-Aviv Yaffo,;Caesarea Rothschild Institute and Department of Computer Science, University of Haifa,
Venue:
Graph-Theoretic Concepts in Computer Science
Year:
2009

Citing 0
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A faster algorithm to recognize even-hole-free graphs

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Finding a smallest odd hole in a claw-free graph using global structure

Discrete Applied Mathematics

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Abstract

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.