On some Graphs with a Unique Perfect Matching
Combinatorics
2017-12-13 v1 Discrete Mathematics
Abstract
We show that deciding whether a given graph of size has a unique perfect matching as well as finding that matching, if it exists, can be done in time if is either a cograph, or a split graph, or an interval graph, or claw-free. Furthermore, we provide a constructive characterization of the claw-free graphs with a unique perfect matching.
Keywords
Cite
@article{arxiv.1712.04228,
title = {On some Graphs with a Unique Perfect Matching},
author = {S. Chaplick and M. Fürst and F. Maffray and D. Rautenbach},
journal= {arXiv preprint arXiv:1712.04228},
year = {2017}
}