Triangle-free planar graphs with the smallest independence number
Combinatorics
2019-03-20 v1 Discrete Mathematics
Abstract
Steinberg and Tovey proved that every n-vertex planar triangle-free graph has an independent set of size at least (n+1)/3, and described an infinite class of tight examples. We show that all n-vertex planar triangle-free graphs except for this one infinite class have independent sets of size at least (n+2)/3.
Keywords
Cite
@article{arxiv.1606.06265,
title = {Triangle-free planar graphs with the smallest independence number},
author = {Zdeněk Dvořák and Tomáš Masařík and Jan Musílek and Ondřej Pangrác},
journal= {arXiv preprint arXiv:1606.06265},
year = {2019}
}
Comments
16 pages, 5 figures