Algorithms for square-3PC(.,.)-free Berge graphs.

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.