SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Discrete Applied Mathematics
Discrete Applied Mathematics
A faster algorithm to recognize even-hole-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Decomposition of even-hole-free graphs with star cutsets and 2-joins
Journal of Combinatorial Theory Series B
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We consider the class ${\cal A}$ of graphs that contain no odd hole, no antihole of length at least $5$, and no prism (a graph consisting of two disjoint triangles with three disjoint paths between them) and the class ${\cal A}'$ of graphs that contain no odd hole, no antihole of length at least $5$, and no odd prism (prism whose three paths are odd). These two classes were introduced by Everett and Reed and are relevant to the study of perfect graphs. We give polynomial-time recognition algorithms for these two classes. In contrast we prove that determining if a general graph contains a prism (or an even prism, or an odd prism) is NP-complete.