New upper bounds for the ramsey numbers r ( k , I ) are obtained. In particular it is shown there is a constant A such that The ramsey number r(k, l ) is the smallest integer n, such that any coloring with red and blue of the edges of the complete graph K , of order n yields either a red K , subgra
An upper bound for the ramsey number r(K5 − e)
✍ Scribed by H. Harborth; I. Mengersen
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 151 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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.
## Abstract Harary stated the conjecture that for any graph __G__ with __n__ edges and without isolated vertices __r__(__K__~3~,__G__) ⩽ 2__n__ + 1. Erdös, Faudree, Rousseau, and Schelp proved that __r__(__K__~3~,__G__) ⩽ ⌈8/3__n__⌉. Here we prove that __r__(__K__~3~,__G__) ⩽ ⌊5/2__n__⌋ −1 for __n_
The kdomination number of a graph G, y k ( G ) , is the least cardinality of a set U of verticies such that any other vertex is adjacent to at least k vertices of U. We prove that if each vertex has degree at least k. then YAG) 5 kp/(k + 1).