Average degree conditions forcing a minor
Combinatorics
2017-07-18 v1
Abstract
Mader first proved that high average degree forces a given graph as a minor. Often motivated by Hadwiger's Conjecture, much research has focused on the average degree required to force a complete graph as a minor. Subsequently, various authors have consider the average degree required to force an arbitrary graph as a minor. Here, we strengthen (under certain conditions) a recent result by Reed and Wood, giving better bounds on the average degree required to force an -minor when is a sparse graph with many high degree vertices. This solves an open problem of Reed and Wood, and also generalises (to within a constant factor) known results when is an unbalanced complete bipartite graph.
Keywords
Cite
@article{arxiv.1506.01775,
title = {Average degree conditions forcing a minor},
author = {Daniel J. Harvey and David R. Wood},
journal= {arXiv preprint arXiv:1506.01775},
year = {2017}
}