New results on maximum induced matchings in bipartite graphs and beyond

Authors:
Konrad K. Dabrowski;Marc Demange;Vadim V. Lozin
Affiliations:
DIMAP & Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK and School of Engineering and Computing Sciences, Durham University, South Road, Durham DH1 3LE, UK;ESSEC Business School, Av. B. Hirsch, 95021 Cergy Pontoise, France and LAMSADE, UMR CNRS 7243, Paris, France;DIMAP & Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

The maximum induced matching problem is known to be APX-hard in the class of bipartite graphs. Moreover, the problem is also intractable in this class from a parameterized point of view, i.e. it is W[1]-hard. In this paper, we reveal several classes of bipartite (and more general) graphs for which the problem admits fixed-parameter tractable algorithms. We also study the computational complexity of the problem for regular bipartite graphs and prove that the problem remains APX-hard even under this restriction. On the other hand, we show that for hypercubes (a proper subclass of regular bipartite graphs) the problem admits a simple solution.