Maximum-Size subgraphs of p4-sparse graphs admitting a perfect matching

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:
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Year:
2005

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Abstract

In this paper, we address the problem of computing a maximum-size subgraph of a P4-sparse graph which admits a perfect matching; in the case where the graph has a perfect matching, the solution to the problem is the entire graph. We establish a characterization of such subgraphs, and describe an algorithm for the problem which for a P4-sparse graph on n vertices and m edges, runs in O(n+m) time and space. The above results also hold for the class of complement reducible graphs or cographs, a well-known subclass of P4-sparse graphs.