On the recognition of probe graphs of some self-complementary classes of perfect graphs

Authors:
Maw-Shang Chang;Ton Kloks;Dieter Kratsch;Jiping Liu;Sheng-Lung Peng
Affiliations:
Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan, R.O.C.;Department of Mathematics and Computer Science, The university of Lethbridge, Alberta, Canada;LITA, Université de Metz, Metz Cedex 01, France;Department of Mathematics and Computer Science, The university of Lethbridge, Alberta, Canada;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan, R.O.C.
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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Abstract

In this paper we consider the recognition of some probe graph classes. Given a class of graphs $\mathcal{G}$, a graph G is a probe graph of $\mathcal{G}$ if its vertices can be partitioned into a set ℙ of probes and an independent set ℕ of nonprobes, such that G can be extended to a graph of $\mathcal{G}$ by adding edges between certain nonprobes. We show that there are polynomial-time recognition algorithms for probe cographs, probe P4-reducible graphs, probe P4-sparse graphs, and probe splitgraphs.