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Upper bounds for ramsey numbers R(3, 3, ⋖, 3) and Schur numbers
Author(s) -
Wan Honghui
Publication year - 1997
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199711)26:3<119::aid-jgt1>3.0.co;2-u
Subject(s) - mathematics , combinatorics , upper and lower bounds , bounded function , graph , ramsey's theorem , schur's theorem , discrete mathematics , classical orthogonal polynomials , mathematical analysis , gegenbauer polynomials , orthogonal polynomials
In this paper we show that for n ≥ 4, R (3, 3, ⋖, 3) < $n!({e-e^{-1}\; +\; 3}\over{2})$ + 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 < $n!({e - e^{-1}\; +\; 3}\over{2})$ ‐ n + 2. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 119–122, 1997