# Algorithms for square-3PC($\cdot, \cdot$)-free Berge graphs

Maffrey, F, Trotignon, N and Vuskovic, K (2008) Algorithms for square-3PC($\cdot, \cdot$)-free Berge graphs. SIAM Journal on Discrete Mathematics, 22 (1). 51 - 71 . ISSN 0895-4801

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We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This class generalizes claw-free Berge graphs and square-free Berge graphs. We give a combinatorial algorithm of complexity $O(n^{7})$ to find a clique of maximum weight in such a graph. We also consider several subgraph-detection problems related to this class.