Odd hole recognition in graphs of bounded clique size

Conforti, M., Cornuéjols, G., Liu, X., Vuskovic, K. & Zambelli, G. (2006). Odd hole recognition in graphs of bounded clique size. SIAM Journal on Discrete Mathematics, 20(1), 42-48. https://doi.org/10.1137/S089548010444540X
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In a graph $G$, an odd hole is an induced odd cycle of length at least 5. A clique of $G$ is a set of pairwise adjacent vertices. In this paper we consider the class ${\cal C}_k$ of graphs whose cliques have a size bounded by a constant $k$. Given a graph $G$ in ${\cal C}_k$, we show how to recognize in polynomial time whether $G$ contains an odd hole.

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