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 considered the average degree required to force an arbitrary graph $H$ 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 $H$-minor when $H$ 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 $H$ is an unbalanced complete bipartite graph.
@article{10_37236_5321,
author = {Daniel J. Harvey and David R. Wood},
title = {Average degree conditions forcing a minor},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {1},
doi = {10.37236/5321},
zbl = {1333.05278},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5321/}
}
TY - JOUR
AU - Daniel J. Harvey
AU - David R. Wood
TI - Average degree conditions forcing a minor
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/5321/
DO - 10.37236/5321
ID - 10_37236_5321
ER -
%0 Journal Article
%A Daniel J. Harvey
%A David R. Wood
%T Average degree conditions forcing a minor
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/5321/
%R 10.37236/5321
%F 10_37236_5321
Daniel J. Harvey; David R. Wood. Average degree conditions forcing a minor. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5321
