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Partitioned Probe Comparability Graphs

  • David B. Chandler
  • Maw-Shang Chang
  • Ton Kloks
  • Jiping Liu
  • Sheng-Lung Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)

Abstract

Given a class of graphs \(\cal{G}\), a graph \(\cal\rm{G}\) is a probe graph of \(\cal{G}\) if its vertices can be partitioned into a set ℙ of probes and an independent set ℕ of nonprobes such that \(\cal\rm{G}\) can be embedded into a graph of \(\cal{G}\) by adding edges between certain nonprobes. If the partition of the vertices is a part of the input we call \(\cal\rm{G}\) a partitioned probe graph of \(\cal{G}\). 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 \({\cal\rm{G}}=(\mathbb{P}+\mathbb{N},E)\) is a partitioned probe permutation graph if and only if \(\cal\rm{G}\) is at the same time a partitioned probe graph of comparability and cocomparability graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David B. Chandler
    • 1
  • Maw-Shang Chang
    • 2
  • Ton Kloks
    • 1
  • Jiping Liu
    • 3
  • Sheng-Lung Peng
    • 4
  1. 1.Institute of MathematicsAcademia SinicaTaipei 115Taiwan R.O.C.
  2. 2.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayi 621Taiwan R.O.C.
  3. 3.Department of Mathematics and Computer ScienceThe University of LethbridgeAlbertaCanada
  4. 4.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityHualien 974Taiwan R.O.C.

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