Partitioned probe comparability graphs

Authors:
David B. Chandler;Maw-Shang Chang;Ton Kloks;Jiping Liu;Sheng-Lung Peng
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, United States;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi 621, Taiwan;School of Computing, University of Leeds, Leeds LS2 9JT, UK;Department of Mathematics and Computer Science, The University of Lethbridge, Alberta, T1K 3M4, Canada;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien 974, Taiwan
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

Given a class of graphs G, a graph G is a probe graph of G if its vertices can be partitioned into a set of probes and an independent set of nonprobes such that G can be embedded into a graph of G by adding edges between certain nonprobes. If the partition of the vertices is part of the input, we call G a partitioned probe graph of G. 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 G is a partitioned probe permutation graph if and only if G is at the same time a partitioned probe graph of comparability and cocomparability graphs.