✦ LIBER ✦

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

✍ Scribed by Earl Glen Whitehead Jr.

Publisher: Elsevier Science
Year: 1973
Tongue: English
Weight: 655 KB
Volume: 4
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90174-x

No coin nor oath required. For personal study only.

✦ Synopsis

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;

1. 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 argument proves that no 65vertex coloring nondegenerate with respect to N(3.3,3,3;
exists. Thus 49 < N(3,3,3,3; 2) 5 65.

📜 SIMILAR VOLUMES

Schur numbers and the ramsey numbers N(3

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

✍ Harold Fredricksen 📂 Article 📅 1979 🏛 Elsevier Science 🌐 English ⚖ 53 KB

Algebraic structure of chromatic graphs

Algebraic structure of chromatic graphs associated with the ramsey number N(3,3,3;2)

✍ Earl Glen Whitehead Jr. 📂 Article 📅 1971 🏛 Elsevier Science 🌐 English ⚖ 116 KB

Notes on the Ramsey number N(3, 3, 3, 3)

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

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.

The irredundant ramsey number s(3, 7)

✍ Guantao Chen; Cecil C. Rousseau 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 395 KB

## Abstract The irredundant Ramsey number __s__(__m, n__) is the smallest __p__ such that for every graph __G__ with __p__ vertices, either __G__ contains an __n__‐element irredundant set or its complement __G__ contains an __m__‐element irredundant set. Cockayne, Hattingh, and Mynhardt have given

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.