On Probe Permutation Graphs

  • David B. Chandler
  • Maw-Shang Chang
  • Antonius J. J. Kloks
  • Jiping Liu
  • Sheng-Lung Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


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(n 2) where n is the number of vertices in the input graph. We show that there are at most O(n 4) 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.


Interval Graph Input Graph Chordal Graph Prime Graph Graph Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David B. Chandler
    • 1
  • Maw-Shang Chang
    • 2
  • Antonius J. J. Kloks
    • 1
  • Jiping Liu
    • 3
  • Sheng-Lung Peng
    • 4
  1. 1.Institute of MathematicsAcademia SinicaNangang, TaipeiTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan
  3. 3.Department of Mathematics and Computer ScienceUniversity of LethbridgeAlbertaCanada
  4. 4.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityHualienTaiwan

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