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 give a structural description of the class C of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected graph in C is a either in some simple basic class or has a decomposition. Basic classes are cliques, bipartite graphs with...

We give a structural description of the class C of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected graph in C is a either in some simple basic class or has a decomposition. Basic classes are cliques, bipartite graphs with...

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...