UPPER-BOUNDS FOR RAMSEY NUMBERS R(3, 3, ..., 3) AND SCHUR NUMBERS

Authors
WAN HH
Citation
Hh. Wan, UPPER-BOUNDS FOR RAMSEY NUMBERS R(3, 3, ..., 3) AND SCHUR NUMBERS, Journal of graph theory, 26(3), 1997, pp. 119-122
Citations number
14
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of graph theory → ACNP
ISSN journal
03649024
Volume
26
Issue
3
Year of publication
1997
Pages
119 - 122
Database
ISI
SICI code
0364-9024(1997)26:3<119:UFRNR3>2.0.ZU;2-4
Abstract
In this paper we show that for n equal to or greater than 4, R(3, 3,.. .,3) < n!(e-e(-1)+3 /2) + 1. Consequently, a new bound for Schur numbe rs is also given. Also, for even n equal to or greater than 6, the Sch ur number S-n is bounded by S-n < n!(e-e(-1)+3 /2) -n+2. (C) 1997 John Wiley & Sons, Inc.