Matchings in 1-planar graphs with large minimum degree
Discrete Mathematics
2020-02-21 v2 Combinatorics
Abstract
In 1979, Nishizeki and Baybars showed that every planar graph with minimum degree 3 has a matching of size (where the constant depends on the connectivity), and even better bounds hold for planar graphs with minimum degree 4 and 5. In this paper, we investigate similar matching-bounds for {\em 1-planar} graphs, i.e., graphs that can be drawn such that every edge has at most one crossing. We show that every 1-planar graph with minimum degree 3 has a matching of size at least , and this is tight for some graphs. We provide similar bounds for 1-planar graphs with minimum degree 4 and 5, while the case of minimum degree 6 and 7 remains open.
Cite
@article{arxiv.1911.04603,
title = {Matchings in 1-planar graphs with large minimum degree},
author = {Therese Biedl and John Wittnebel},
journal= {arXiv preprint arXiv:1911.04603},
year = {2020}
}