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Minors in Graphs with High Chromatic Number

Published online by Cambridge University Press:  13 April 2011

THOMAS BÖHME
Affiliation:
Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany (e-mail: tboehme@theoinf.tu-ilmenau.de)
ALEXANDR KOSTOCHKA
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk, Russia (e-mail: kostochk@math.uiuc.edu)
ANDREW THOMASON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK (e-mail: A.G.Thomason@dpmms.cam.ac.uk)

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) ≥ (4kn)/3.

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Copyright © Cambridge University Press 2011

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References

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