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

✍ Scribed by Jon Folkman

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
388 KB
Volume
16
Category
Article
ISSN
0097-3165

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πŸ“œ SIMILAR VOLUMES

The ramsey number N(3, 3, 3, 3; 2)
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✍ Earl Glen Whitehead Jr. πŸ“‚ Article πŸ“… 1973 πŸ› Elsevier Science 🌐 English βš– 655 KB

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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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)
The irredundant ramsey number s(3, 7)
✍ Guantao Chen; Cecil C. Rousseau πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 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,
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✍ Wan, Honghui πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 81 KB πŸ‘ 2 views

In this paper we show that for n β‰₯ 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 β‰₯ 6, the Schur number S n is bounded by S n < n!( e-e -1 + 3 2 ) -n + 2.