On the Induced Matching Problem in Hamiltonian Bipartite Graphs

In this paper, we study the parameterized complexity and inapproximability of the Induced Matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian cycle in a hamiltonian bipartite graph, the problem is W[1]-hard and cannot be solved in time n 1 2 ) unless W[1]=FPT, where n is the number of vertices in the graph. In addition, we show that unless NP=P, the maximum induced matching in a hamiltonian graph cannot be approximated within a ratio of n, where n is the number of vertices in the graph. For a bipartite hamiltonian graph in n vertices, it is NP-hard to approximate its maximum induced matching based on a hamiltonian cycle of the graph within a ratio of n 1 4 , where n is the number of vertices in the graph and ǫ is any positive constant.