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Schur numbers and the ramsey numbers N(3, 3,…, 3; 2)

✍ Scribed by Harold Fredricksen

Publisher: Elsevier Science
Year: 1979
Tongue: English
Weight: 53 KB
Volume: 27
Category: Article
ISSN: 0097-3165
DOI: 10.1016/0097-3165(79)90028-1

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📜 SIMILAR VOLUMES

Upper bounds for ramsey numbers R(3, 3,

Upper bounds for ramsey numbers R(3, 3, ?, 3) and Schur numbers

✍ Wan, Honghui 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 81 KB 👁 2 views

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.

The ramsey number N(3, 3, 3, 3; 2)

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A partition of the nonzero elements of the finite abelian group Z/72 X Z/72 into four sum-free sets shows that N (3,3,3,3; 2) > 49. Based on a matrix technique for analyzing the structure of the two nonisomorphic 16-vertex edge-coiorings nondegenerate with respect to N(3,3,3;2), an involved argumen

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✍ Jon Folkman 📂 Article 📅 1974 🏛 Elsevier Science 🌐 English ⚖ 388 KB

Zero-Sum Ramsey Numbers modulo 3

✍ Heiko Harborth; Lothar Piepmeyer 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 184 KB

Simple proofs are given for three infinite classes of zero-sum Ramsey numbers modulo 3: r(K n , Z 3 )=n+3 for n#1, 4 (mod 9) and r(K n , Z 3 )=n+4 for n#0 (mod 9).

An improved upper bound for Ramsey numbe

An improved upper bound for Ramsey number N (3, 3, 3, 3; 2)

✍ Adolfo Sanchez-Flores 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 251 KB

The Ramsey number N(3, 3, 3, 3; 2) is the smallest integer n such that each 4-coloring by edges of the complete graph on n vertices contains monochromatic triangles. It is well known that 51 ~< N(3,3,3,3;2) ~< 65. Here we prove that N(3,3,3,3;2) ~< 64.

On ramsey-tuŕan numbers for 3-graphs

✍ A. F. Sidorenko 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 255 KB

## Abstract For every __r__‐graph __G__ let π(__G__) be the minimal real number ϵ such that for every ϵ < 0 and __n__ ϵ __n__~0~(λ, __G__) every __R__‐graph __H__ with __n__ vertices and more than (π + ϵ)(nr) edges contains a copy of __G__. The real number λ(__G__) is defined in the same way, addin