On Ramsey numbers of uniform hypergraphs with given maximum degree

A. V. Kostochka; V. Rödl

doi:10.1016/j.jcta.2005.12.007

On Ramsey numbers of uniform hypergraphs with given maximum degree

A. V. Kostochka, V. Rödl

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For every ε{lunate} > 0 and every positive integers Δ and r, there exists C = C (ε{lunate}, Δ, r) such that the Ramsey number, R (H, H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C | V (H) |^{1 + ε{lunate}}.

Original language	English (US)
Pages (from-to)	1555-1564
Number of pages	10
Journal	Journal of Combinatorial Theory. Series A
Volume	113
Issue number	7
DOIs	https://doi.org/10.1016/j.jcta.2005.12.007
State	Published - Oct 2006

Keywords

Maximum degree
Ramsey numbers
Uniform hypergraphs

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Online availability

10.1016/j.jcta.2005.12.007

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title = "On Ramsey numbers of uniform hypergraphs with given maximum degree",

abstract = "For every ε{lunate} > 0 and every positive integers Δ and r, there exists C = C (ε{lunate}, Δ, r) such that the Ramsey number, R (H, H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C | V (H) |1 + ε{lunate}.",

keywords = "Maximum degree, Ramsey numbers, Uniform hypergraphs",

author = "Kostochka, {A. V.} and V. R{\"o}dl",

note = "Funding Information: E-mail address: [email protected] (V. R{\"o}dl). 1 Research of the author was supported by the NSF grant DMS-0400498 and grant 03-01-00796 of the Russian Foundation for Fundamental Research. 2 Research of the author was supported by the NSF grant DMS-0300529.",

year = "2006",

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AU - Kostochka, A. V.

AU - Rödl, V.

N1 - Funding Information: E-mail address: [email protected] (V. Rödl). 1 Research of the author was supported by the NSF grant DMS-0400498 and grant 03-01-00796 of the Russian Foundation for Fundamental Research. 2 Research of the author was supported by the NSF grant DMS-0300529.

PY - 2006/10

Y1 - 2006/10

N2 - For every ε{lunate} > 0 and every positive integers Δ and r, there exists C = C (ε{lunate}, Δ, r) such that the Ramsey number, R (H, H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C | V (H) |1 + ε{lunate}.

AB - For every ε{lunate} > 0 and every positive integers Δ and r, there exists C = C (ε{lunate}, Δ, r) such that the Ramsey number, R (H, H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C | V (H) |1 + ε{lunate}.

KW - Maximum degree

KW - Ramsey numbers

KW - Uniform hypergraphs

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ER -

On Ramsey numbers of uniform hypergraphs with given maximum degree

Abstract

Keywords

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