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Hypergraph Packing and Sparse Bipartite Ramsey Numbers

Published online by Cambridge University Press:  22 June 2009

DAVID CONLON
DAVID CONLON*
Affiliation:
St John's College, Cambridge CB2 1TP, UK (e-mail: D.Conlon@dpmms.cam.ac.uk)
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Abstract

We prove that there exists a constant c such that, for any integer Δ, the Ramsey number of a bipartite graph on n vertices with maximum degree Δ is less than 2cΔn. A probabilistic argument due to Graham, Rödl and Ruciński implies that this result is essentially sharp, up to the constant c in the exponent. Our proof hinges upon a quantitative form of a hypergraph packing result of Rödl, Ruciński and Taraz.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 6 , November 2009 , pp. 913 - 923
Copyright
Copyright © Cambridge University Press 2009

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