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(n7) to find a clique of maximum weight in such a graph. We also consider several subgraph-detection problems related to this class.
@article{arxiv.1309.0694,
title = {Algorithms for square-$3PC(\cdot, \cdot)$-free Berge graphs},
author = {Frédéric Maffray and Nicolas Trotignon and Kristina Vušković},
journal= {arXiv preprint arXiv:1309.0694},
year = {2016}
}