text: abstract
  we address the induced matching enumeration problem. an edge set m is an induced
  matching of a graph g = (v, e). the enumeration of matchings are widely studied in literature, but the induced matching has not been paid much attention. a straightforward
  algorithm takes o (|v |) time for each solution, that is coming from the time to generate a
  subproblem. we investigated local structures that enables us to generate subproblems in
  short time, and proved that the time complexity will be o (1) if the input graph is c4 -free.
  a c4 -free graph is a graph any whose subgraph is not a cycle of length four. finally, we
  show the fixed parameter tractability of counting induced matchings for graphs with bounded
  tree-width and planar graphs.