A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that every Berge graph either is in a well...

We prove that the problem of deciding whether a graph has a balanced skew partition is NP-hard. We give an O(n9)-time algorithm for the same problem restricted to Berge graphs. Our algorithm is not constructive : it certifies that a graph has a balanced skew partition if it has one. It relies on...

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...

A hole in a graph is an induceed cycle on at least four vertices. A graph is Berge if it has no old hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that every Berge graph either is in a well...