Finding a maximum induced matching in weakly chordal graphs

Authors:
Kathie Cameron;R. Sritharan;Yingwen Tang
Affiliations:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ont., Canada N2L 3C5;Computer Science Department, University of Dayton, Dayton, OH;Computer Science Department, University of Dayton, Dayton, OH
Venue:
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Year:
2003

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Abstract

An induced matching in a graph G is a set of edges, no two of which meet a common vertex or are joined by an edge of G; that is, an induced matching is a matching which forms an induced subgraph. It is known that finding an induced matching of maximum cardinality in a graph is NP-hard. We show that a maximum induced matching in a weakly chordal graph can be found in polynomial time. This generalizes previously known results for the induced matching problem. This also demonstrates that the maximum induced matching problem in chordal bipartite graphs can be solved in polynomial time while the problem is known to be NP-hard for bipartite graphs in general.