On probe permutation graphs

Authors:
David B. Chandler;Maw-Shang Chang;Ton Kloks;Jiping Liu;Sheng-Lung Peng
Affiliations:
-;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi 621, Taiwan;-;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:
Discrete Applied Mathematics
Year:
2009

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Abstract

Given a class of graphs G, a graph G is a probe graph ofG if its vertices can be partitioned into two sets, P, the probes, and an independent set N, the nonprobes, such that G can be embedded into a graph of G by adding edges between certain vertices of N. If the partition of the vertices into probes and nonprobes is part of the input, then we call the graph a partitioned probe graph ofG. In this paper, we provide a recognition algorithm for partitioned probe permutation graphs with time complexity O(n^2), where n is the number of vertices of the input graph. We show that a probe permutation graph has at most O(n^4) minimal separators. As a consequence, for probe permutation graphs there exist polynomial-time algorithms solving problems like treewidth and minimum fill-in. We also characterize those graphs for which the probe graphs must be weakly chordal.