English

Finding big matchings in planar graphs quickly

Data Structures and Algorithms 2019-02-22 v1 Combinatorics

Abstract

It is well-known that every nn-vertex planar graph with minimum degree 3 has a matching of size at least n3\frac{n}{3}. But all proofs of this use the Tutte-Berge-formula for the size of a maximum matching. Hence these proofs are not directly algorithmic, and to find such a matching one must apply a general-purposes maximum matching algorithm, which has run-time O(n1.5α(n))O(n^{1.5}\alpha(n)) for planar graphs. In contrast to this, this paper gives a linear-time algorithm that finds a matching of size at least n3\frac{n}{3} in any planar graph with minimum degree 3.

Keywords

Cite

@article{arxiv.1902.07812,
  title  = {Finding big matchings in planar graphs quickly},
  author = {Therese Biedl},
  journal= {arXiv preprint arXiv:1902.07812},
  year   = {2019}
}
R2 v1 2026-06-23T07:46:34.020Z