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Recognition of Probe Ptolemaic Graphs

(Extended Abstract)
  • Maw-Shang Chang
  • Ling-Ju Hung
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

Let \(\mathcal{G}\) denote a graph class. An undirected graph G is called a probe \(\mathcal{G}\) graph if one can make G a graph in \(\mathcal{G}\) by adding edges between vertices in some independent set of G. By definition graph class \(\mathcal{G}\) is a subclass of probe \(\mathcal{G}\) graphs. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distance-hereditary graphs. Many problems NP-hard on chordal graphs can be solved in polynomial time on ptolemaic graphs. We proposed an O(nm)-time algorithm to recognize probe ptolemaic graphs where n and m are the numbers of vertices and edges of the input graph respectively.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Maw-Shang Chang
    • 1
  • Ling-Ju Hung
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan

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