English

On some Graphs with a Unique Perfect Matching

Combinatorics 2017-12-13 v1 Discrete Mathematics

Abstract

We show that deciding whether a given graph GG of size mm has a unique perfect matching as well as finding that matching, if it exists, can be done in time O(m)O(m) if GG 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}
}
R2 v1 2026-06-22T23:15:25.104Z