English

The extremal function for Petersen minors

Combinatorics 2019-08-13 v3

Abstract

We prove that every graph with nn vertices and at least 5n85n-8 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 5n115n-11 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}
}
R2 v1 2026-06-22T10:36:41.494Z