The parameterized complexity of the induced matching problem ? ??
Given a graph G G and an integer k?0 k ? 0 , the NP-complete Induced Matching problem asks whether there exists an edge subset M M of size at least k k such that M M is a matching and no two edges of M M are joined by an edge of G G . The complexity of this problem on general graphs, as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W W [1]-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.
parameterized complexity induced matching planar graph kernelization tree decomposition