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Off-diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)

✍ Scribed by Roland Lortz; Ingrid Mengersen

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 210 KB
Volume: 43
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10118

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✦ Synopsis

Abstract

An upper bound on the Ramsey number r(K~2,n‐s~,K~2,n~) where s ≥ 2 is presented. Considering certain r(K~2,n‐s~,K~2,n~)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of r(K~2,n‐s~,K~2,n~) in infinitely many cases if $s \approx 2\sqrt n$ holds. Moreover, the asymptotic behavior of r(K~2,m~,K~2,n~) is studied for n being sufficiently large depending on m. We conclude with a table of all known Ramsey numbers r(K~2,m~,K~2,n~) where m,n ≤ 10. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 252–268, 2003

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