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Probe Ptolemaic Graphs

  • David B. Chandler
  • Maw-Shang Chang
  • Ton Kloks
  • Van Bang Le
  • Sheng-Lung Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

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 nonprobes. In this paper we study the probe graphs of ptolemaic graphs when the partition of vertices is unknown. We present some characterizations of probe ptolemaic graphs and show that there exists a polynomial-time recognition algorithm for probe ptolemaic graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • David B. Chandler
    • 1
  • Maw-Shang Chang
    • 2
  • Ton Kloks
    • 1
  • Van Bang Le
    • 3
  • Sheng-Lung Peng
    • 4
  1. 1.Department of Mathematical SciencesUniversity of Delaware NewarkDelawareUSA
  2. 2.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan
  3. 3.Institut für InformatikUniversität RostockRostockGermany
  4. 4.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityHualienTaiwan

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