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When is an Almost Monochromatic K4 Guaranteed?

Published online by Cambridge University Press:  01 November 2008

ALEXANDR KOSTOCHKA  and
DHRUV MUBAYI
ALEXANDR KOSTOCHKA
Affiliation:
Department of Mathematics, University of Illinois, Urbana, USA and Institute of Mathematics, Novosibirsk, Russia (e-mail: kostochk@math.uiuc.edu)
DHRUV MUBAYI
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois, 851 S. Morgan Street, Chicago, IL 60607-704, USA (e-mail: mubayi@math.uic.edu)
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Abstract

Suppose that n > (log k)ck, where c is a fixed positive constant. We prove that, no matter how the edges of Kn are coloured with k colours, there is a copy of K4 whose edges receive at most two colours. This improves the previous best bound of kc′k, where c′ is a fixed positive constant, which follows from results on classical Ramsey numbers.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 6 , November 2008 , pp. 823 - 830
Copyright
Copyright © Cambridge University Press 2008

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