A good characterization of cograph contractions

A graph is called a cograph contraction if it is obtained from a cograph (a graph with no induced path on four vertices) by contracting some pairwise disjoint independent sets and then making the ‘‘contracted’’ vertices pairwise adjacent. Cograph contractions are perfect and generalize cographs and split graphs. This article gives a good characterization of cograph contractions, solving a problem posed by M. Hujter and Zs. Tuza. c © 1999 John Wiley & Sons, Inc. J Graph Theory 30: