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 is an induced matching of a graph . The enumeration of matchings are widely studied in literature, but the induced matching has not been paid much attention. A straightforward algorithm takes 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 if the input graph is -free. A -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}
}