English

Efficient Enumeration of Induced Matchings in a Graph without Cycles with Length Four

Data Structures and Algorithms 2018-09-21 v1

Abstract

We address the induced matching enumeration problem. An edge set MM is an induced matching of a graph G=(V,E)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)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)O(1) if the input graph is C4C_4-free. A C4C_4-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.

Keywords

Cite

@article{arxiv.1707.02740,
  title  = {Efficient Enumeration of Induced Matchings in a Graph without Cycles with Length Four},
  author = {Kazuhiro Kurita and Kunihiro Wasa and Takeaki Uno and Hiroki Arimura},
  journal= {arXiv preprint arXiv:1707.02740},
  year   = {2018}
}