An O(n3)-Time Recognition Algorithm for hhds-free Graphs

  • Authors:

  • Elaine M. Eschen;Chính T. Hoàng;R. Sritharan

  • Affiliations:

  • West Virginia University, Lane Department of Computer Science and Electrical Engineering, 26506, Morgantown, WV, USA;Wilfrid Laurier University, Department of Physics and Computer Science, N2L 3C5, Waterloo, ON, Canada;The University of Dayton, Computer Science Department, 45469, Dayton, OH, USA

  • Venue:
  • Graphs and Combinatorics
  • Year:
  • 2007

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Abstract

The class of hhds-free graphs properly generalizes the classes of strongly chordal graphs and distance-hereditary graphs, and forms a restriction of the class of perfectly orderable graphs. The problem of recognizing hhds-free graphs in polynomial time was posed by Brandstädt (Problem session, Dagstuhl seminor No. 04221, 2004), and Nikolopoulos and Palios (Proceedings of the 31st International Workshop on Graph Theoretic Concepts in Computer Science, 2005) gave an O(mn2) algorithm. We present an O(n3)-time algorithm for the problem. Our algorithm demonstrates a relationship between hhds-free graphs and strongly chordal graphs similar to that which is known to exist between hhd-free graphs and chordal graphs.