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Minors in Graphs with High Chromatic Number

Published online by Cambridge University Press:  13 April 2011

THOMAS BÖHME ,
ALEXANDR KOSTOCHKA  and
ANDREW THOMASON
THOMAS BÖHME
Affiliation:
Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany (e-mail: [email protected])
ALEXANDR KOSTOCHKA
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk, Russia (e-mail: [email protected])
ANDREW THOMASON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK (e-mail: [email protected])
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Abstract

We develop lower bounds on the Hadwiger number h(G) of graphs G with high chromatic number. In particular, if G has n vertices and chromatic number k then h(G) ≥ (4k − n)/3.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 4 , July 2011 , pp. 513 - 518
Copyright
Copyright © Cambridge University Press 2011

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