The extremal function for Petersen minors
Combinatorics
2019-08-13 v3
Abstract
We prove that every graph with vertices and at least edges contains the Petersen graph as a minor, and this bound is best possible. Moreover we characterise all Petersen-minor-free graphs with at least edges. It follows that every graph containing no Petersen minor is 9-colourable and has vertex arboricity at most 5. These results are also best possible.
Keywords
Cite
@article{arxiv.1508.04541,
title = {The extremal function for Petersen minors},
author = {Kevin Hendrey and David R. Wood},
journal= {arXiv preprint arXiv:1508.04541},
year = {2019}
}