Minimum maximal matching is NP-hard in regular bipartite graphs

Authors:
M. Demange;T. Ekim
Affiliations:
ESSEC Business School, Cergy Pontoise cedex, France;Boǧaziçi University, Department of Industrial Engineering, Bebek-Istanbul, Turkey
Venue:
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Year:
2008

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Abstract

Yannakakis and Gavril showed in [10] that the problem of finding a maximal matching of minimum size (MMM for short), also called Minimum Edge Dominating Set, is NP-hard in bipartite graphs of maximum degree 3 or planar graphs of maximum degree 3. Horton and Kilakos extended this result to planar bipartite graphs and planar cubic graphs [6]. Here, we extend the result of Yannakakis and Gavril in [10] by showing that MMM is NP-hard in the class of k-regular bipartite graphs for all k ≥ 3 fixed.