Partitioned probe comparability graphs

Authors:
David B. Chandler;Maw-Shang Chang;Ton Kloks;Jiping Liu;Sheng-Lung Peng
Affiliations:
Institute of Mathematics, Academia Sinica, Taipei 115, Taiwan R.O.C.;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi 621, Taiwan R.O.C.;Institute of Mathematics, Academia Sinica, Taipei 115, Taiwan R.O.C.;Department of Mathematics and Computer Science, The University of Lethbridge, Alberta, Canada;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien 974, Taiwan R.O.C.
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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Abstract

Given a class of graphs , a graph is a probe graph of if its vertices can be partitioned into a set ℙ of probes and an independent set ℕ of nonprobes such that can be embedded into a graph of by adding edges between certain nonprobes. If the partition of the vertices is a part of the input we call a partitioned probe graph of . In this paper we show that there exists a polynomial-time algorithm for the recognition of partitioned probe graphs of comparability graphs. This immediately leads to a polynomial-time algorithm for the recognition of partitioned probe graphs of cocomparability graphs. We then show that a partitioned graph is a partitioned probe permutation graph if and only if is at the same time a partitioned probe graph of comparability and cocomparability graphs.