The PIGs full monty – a floor show of minimal separators

Authors:
Gerard Jennhwa Chang;Antonius J. J. Kloks;Jiping Liu;Sheng-Lung Peng
Affiliations:
Department of Mathematics, National Taiwan University, Taipei, Taiwan;Department of Mathematics, National Taiwan University, Taipei, Taiwan;Department of Mathematics and Computer Science, The university of Lethbridge, Alberta, Canada;Department of Computer Science and Electrical Engineering, National Dong Hwa University, Hualien, Taiwan
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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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 (non–probes), 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. We show that the recognition problem of probe interval graphs, i.e., probe graphs of the class of interval graphs, is in P.