Finding big matchings in planar graphs quickly
Data Structures and Algorithms
2019-02-22 v1 Combinatorics
Abstract
It is well-known that every -vertex planar graph with minimum degree 3 has a matching of size at least . 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 for planar graphs. In contrast to this, this paper gives a linear-time algorithm that finds a matching of size at least in any planar graph with minimum degree 3.
Cite
@article{arxiv.1902.07812,
title = {Finding big matchings in planar graphs quickly},
author = {Therese Biedl},
journal= {arXiv preprint arXiv:1902.07812},
year = {2019}
}