Maximum vertex-weighted matching in strongly chordal graphs

Abstract

Given a graph G = ( V, E) and a real weight for each vertex of G, the vertex-weight of a matching is defined to be the sum of the weights of the vertices covered by the matching. In this paper we present a linear time algorithm for finding a maximum vertex-weighted matching in a strongly chordal graph, given a strong elimination ordering. The algorithm can be specialized to find a maximum cardinality matching, yielding an algorithm similar to one proposed earlier by Dahlhaus and Karpinsky. The technique does not seem to apply to the case of general edge-weighted matchings.