The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

Abstract. Given a graph G and a nonnegative integer k, the NP-complete Induced Matching problem asks for an edge subset M 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 on many restricted graph classes has been studied intensively. However, little is known about the parameterized complexity of this problem. Our main contribution for the problem—which is W[1]-hard in general—is to show that it is fixed-parameter tractable on planar graphs by providing a linear problem kernel. Additionally, we generalize a known algorithm for Induced Matching on trees to graphs of bounded treewidth using an improved dynamic programming approach.

• Type: Conference
• Year: 2007
• Where: FAW
• Authors: Hannes Moser, Somnath Sikdar
• Keywords: FAW 2007, Linear Problem Kernel, Nonnegative Integer, NP-complete Induced Matching