# 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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## Abstract

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.

Item Type: Article The University of Leeds The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) Mrs Irene Rudling 22 Oct 2012 13:01 08 Feb 2013 17:39 http://dx.doi.org/10.1137/050628520 Published Society for Industrial and Applied Mathematics Yes 10.1137/050628520 http://eprints.whiterose.ac.uk/id/eprint/74366