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 Brandstadt (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(m n 2) algorithm. We present an O(n 3)-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.

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