The parameterized complexity of the induced matching problem

Given a graph G and an integer k >= 0, the NP-complete INDUCED MATCHING problem asks whether there exists ail edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs, as well as oil many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[l]-hard on general graphs, little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we provide first-time fixed-parameter tractability results for planar graphs, bounded-degree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth. In particular, we give a linear-size problem kernel for planar graphs. (C) 2008 Elsevier B.V. All rights reserved.