  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.
