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arXiv · 1311.0358

A Faster Algorithm to Recognize Even-Hole-Free Graphs

Hsien-Chih Chang·Hsueh-I Lu
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Abstract

We study the problem of determining whether an $n$-node graph $G$ has an even hole, i.e., an induced simple cycle consisting of an even number of nodes. Conforti, Cornu\'ejols, Kapoor, and Vu\v{s}kovi\'c gave the first polynomial-time algorithm for the problem, which runs in $O(n^{40})$ time. Later, Chudnovsky, Kawarabayashi, and Seymour reduced the running time to $O(n^{31})$. The best previously known algorithm for the problem, due to da Silva and Vu\v{s}kovi\'c, runs in $O(n^{19})$ time. In this paper, we solve the problem in $O(n^{11})$ time. Moreover, if $G$ has even holes, our algorithm also outputs an even hole of $G$ in $O(n^{11})$ time.

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Hsien-Chih Chang, Hsueh-I Lu. 2013-11-02. A Faster Algorithm to Recognize Even-Hole-Free Graphs. https://doi.org/10.1016/j.jctb.2015.02.001

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