Fast Skew Partition Recognition

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Chvátal defined a skew partition of a graph G to be a partition of its vertex set into two non-empty parts A and B such that A induces a disconnected subgraph of G and B induces a disconnected subgraph of \(\overline{G}\) . Skew partitions are important in the characterization of perfect graphs. De Figuereido et al. presented a polynomial time algorithm which given a graph either finds a skew partition or determines that no such partition exists. It runs in O(n 101) time. We present an algorithm for the same problem which runs in O(n 4 m) time.