Induced Packing of Odd Cycles in a Planar Graph
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A faster algorithm to recognize even-hole-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Induced packing of odd cycles in planar graphs
Theoretical Computer Science
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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.