Induced Matchings in Regular Graphs and Trees

This paper studies the complexity of the Maximum Induced Matching problem (MIM) in regular graphs and trees. We show that the largest induced matchings in a regular graph of degree d can be approximated with a performance ratio less than d. However MIM is NP-hard to approximate within some constant c > 1 even if the input is restricted to various classes of bounded degree and regular graphs. Finally we describe a simple algorithm providing a linear time optimal solution to MIM if the input graph is a tree.