๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Number of Monochromatic Schur Triples

โœ Scribed by Tomasz Schoen

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
127 KB
Volume
20
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper, we prove that in every 2-coloring of the set {1, . . . , N } = R โˆช B, one can find at least N 2 /22 + O(N ) monochromatic solutions of the equation x + y = z. This solves a problem of Graham et al. [1].

๐Ÿ“œ SIMILAR VOLUMES

The number of edge colorings with no mon
The number of edge colorings with no monochromatic triangle
โœ Yuster, Raphael ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 639 KB

Let F(n, k) denote the maximum number of t w o edge colorings of a graph on n vertices that admit no monochromatic Kk. la complete graph on k vertices). The following results are proved: f ( n , 3) = 2Ln2/41 for all n 2 6. f ( n , k) = 2((k~2)/(2k-2)+o( 1))n'. In particular, the first result solves

On the number of steiner triple systems
On the number of steiner triple systems
โœ V. E. Alekseev ๐Ÿ“‚ Article ๐Ÿ“… 1974 ๐Ÿ› SP MAIK Nauka/Interperiodica ๐ŸŒ English โš– 225 KB
On the chromatic numbers of Steiner trip
On the chromatic numbers of Steiner triple systems
โœ Lucien Haddad ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 188 KB ๐Ÿ‘ 2 views

Geometric properties are used to determine the chromatic number of AG(4, 3) and to derive some important facts on the chromatic number of PG(n, 2). It is also shown that a 4-chromatic STS(v) exists for every admissible order v โ‰ฅ 21.