@article{4c76a7548b3f45e2b539b35b332e33e5,
title = "Large minors in graphs with given independence number",
abstract = "A weakening of Hadwiger's conjecture states that every n-vertex graph with independence number α has a clique minor of size at least nα. Extending ideas of Fox (2010) [6], we prove that such a graph has a clique minor with at least n(2-c)α vertices where c>119.2.",
keywords = "Clique minor, Hadwiger's conjecture, Independence number",
author = "J{\'o}zsef Balogh and Kostochka, {A. V.}",
note = "Funding Information: The second author{\textquoteright}s research was supported in part by NSF grant DMS-0965587 and by the Ministry of education and science of the Russian Federation (Contract no. 14.740.11.0868). Funding Information: The first author{\textquoteright}s research was supported in part by NSF CAREER Grant DMS-0745185 , UIUC Campus Research Board Grants 09072 and 11067 , OTKA Grant K76099 , and TAMOP-4.2.1/B-09/1/KONV-2010-0005 project. ",
year = "2011",
month = oct,
day = "28",
doi = "10.1016/j.disc.2011.07.003",
language = "English (US)",
volume = "311",
pages = "2203--2215",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "20",
}