An O(nm)-time certifying algorithm for recognizing HHD-free graphs

Authors:
Stavros D. Nikolopoulos;Leonidas Palios
Affiliations:
Department of Computer Science, University of Ioannina, Ioannina, Greece;Department of Computer Science, University of Ioannina, Ioannina, Greece
Venue:
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Year:
2007

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Abstract

In this paper, we consider the recognition problem on a class of perfectly orderable graphs, namely, the HHD-free graphs, i.e., graphs that do not contain any induced subgraph isomorphic to a house, a hole, or a domino. We prove properties of the HHD-free graphs which enable us to present an O(nm)-time and O(n+m)-space algorithm for determining whether a given graph G on n vertices and m edges is HHD-free. The algorithm can be augmented to provide a certificate (an induced house, hole, or domino) whenever it decides that the input graph is not HHDfree; the certificate computation requires O(n + m) additional time and O(n) space.