Finding skew partitions efficiently

Abstract

A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A, B, C, D such that there are all possible edges between A and B, and no edges between C and D. We present a polynomial-time algorithm for testing whether a graph admits a skew partition. Our algorithm solves the more general list skew partition problem, where the input contains, for each vertex, a list containing some of the labels A, B, C, D of the four parts. Our polynomial-time algorithm settles the complexity of the original partition problem proposed by Chvátal, and answers a recent question of Feder, Hell, Klein and Motwani. © Springer-Verlag Berlin Heidelberg 2000.