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An Upper Bound for Constrained Ramsey Numbers

Published online by Cambridge University Press:  07 June 2006

PETER WAGNER
PETER WAGNER
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK (e-mail: pw236@cam.ac.uk)
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Abstract

Let $s$ and $t$ be integers satisfying $s \geq 2$ and $t \geq 2$. Let $S$ be a tree of size $s$, and let $P_t$ be the path of length $t$. We show in this paper that, for every edge-colouring of the complete graph on $n$ vertices, where $n=224(s-1)^2t$, there is either a monochromatic copy of $S$ or a rainbow copy of $P_t$. So, in particular, the number of vertices needed grows only linearly in $t$.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 4 , July 2006 , pp. 619 - 626
Copyright
2006 Cambridge University Press

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