On probe permutation graphs

Authors:
David B. Chandler;Maw-Shang Chang;Antonius J. J. Kloks;Jiping Liu;Sheng-Lung Peng
Affiliations:
Institute of Mathematics, Academia Sinica, Nangang, Taipei, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan;Institute of Mathematics, Academia Sinica, Nangang, Taipei, Taiwan;Department of Mathematics and Computer Science, University of Lethbridge, Alberta, Canada;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

Citing 12
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Abstract

Given a class of graphs $\mathcal{G}$, a graph G is a probe graph of$\mathcal{G}$ if its vertices can be partitioned into two sets ℙ, the probes, and ℕ, the nonprobes, where ℕ is an independent set, such that G can be embedded into a graph of $\mathcal{G}$ 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 of$\mathcal{G}$. In this paper, we provide a recognition algorithm for partitioned probe permutation graphs with time complexity O(n2) where n is the number of vertices in the input graph. We show that there are at most O(n4) minimal separators for a probe permutation graph. As a consequence, there exist polynomial-time algorithms solving treewidth and minimum fill-in problems for probe permutation graphs.