English

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

R2 v1 2026-06-22T14:29:42.173Z