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Recognition of Probe Cographs and Partitioned Probe Distance Hereditary 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 4041)

Abstract

Given a class of graphs \({\cal G}\), a graph G is a probe graph of \({\cal G}\) if its vertices can be partitioned into two sets ℙ (the probes) and ℕ (nonprobes), where ℕ is an independent set, such that G can be embedded into a graph of \({\cal G}\) 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 \({\cal G}\). We give the first polynomial-time algorithm for recognizing partitioned probe distance-hereditary graphs. By using a novel data structure for storing a multiset of sets of numbers, the running time of this algorithm is \({O}(\mathfrak\it{n}^2)\), where \(\mathfrak\it{n}\) is the number of vertices of the input graph. We also show that the recognition of both partitioned and unpartitioned probe cographs can be done in \({O}(\mathfrak\it{n}^2)\) time.

Keywords

Leaf Node Binary Tree Recognition Algorithm Interval Graph Decomposition Tree 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David B. Chandler
    • 1
  • Maw-Shang Chang
    • 2
  • Ton Kloks
  • Jiping Liu
    • 3
  • Sheng-Lung Peng
    • 4
  1. 1.Institute of MathematicsAcademia Sinica, NangangTaipeiTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan
  3. 3.Department of Mathematics and Computer ScienceThe University of LethbridgeAlbertaCanada
  4. 4.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityHualienTaiwan

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