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New Upper and Lower Bounds for Ramsey Numbers

✍ Scribed by Huang Yi Ru; Yang Jian Sheng

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 76 KB
Volume: 22
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0438

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In this paper we show that for n ≥ 4, R(3, 3, . . . , 3) < n!( e-e -1 + 3 2 ) + 1. Consequently, a new bound for Schur numbers is also given. Also, for even n ≥ 6, the Schur number S n is bounded by S n < n!( e-e -1 + 3 2 ) -n + 2.