Characterisations and linear-time recognition of probe cographs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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A graph is called a graph 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. © John Wiley & Sons, Inc. J Graph Theory 30: 309–318, 1999