A faster algorithm to recognize even-hole-free graphs

Authors:
Hsien-Chih Chang;Hsueh-I Lu
Affiliations:
National Taiwan University;National Taiwan University
Venue:
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Year:
2012

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Abstract

We study the problem of determining whether an n-node m-edge graph has an even hole, i.e., an induced simple cycle consisting of an even number of nodes. Conforti, Cornuéjols, Kapoor, and Vušković gave the first polynomial-time algorithm for the problem, which runs in O(n40) time. Later, Chudnovsky, Kawarabayashi, and Seymour reduced the running time to O(n31). The best previously known algorithm for the problem, due to da Silva and Vušković, runs in O(n19) time. In this paper, we solve the problem in time O(n11).