## Abstract The following result is proved. A graph __G__ can be expressed as the edgeβdisjoint union of __k__ graphs having chromatic numbers no greater than __m__~1~,β¦,__m__~__k__~, respectively, iff Ο(__G__) β€ __m__~1~β¦__m__~__k__~.
A result on C4-star Ramsey numbers
β Scribed by Guantao Chen
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 140 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we will show that the Ramsey number r(C4,Ki,n+l)<~r(C4,Ki,n)+ 2 for all positive integers n. This result answers a question proposed by Burr, Erd6s, Faudree, Rousseau, and Schelp.
π SIMILAR VOLUMES
Caro, Y., On zero-sum Ramsey numbers--stars, Discrete Mathematics 104 (1992) l-6. Let n 3 k 2 2 be positive integers, k ( n. Let H, be the cyclic group of order k. Denote by R(K,,,> Z,) the minimal integer t such that for every &-coloring of the edges of K,, (i.e., a function c : E(K,)+ hk), there i
The multicolor Ramsey number r k (C 4 ) is the smallest integer n for which any k-coloring of the edges of the complete graph K n must produce a monochromatic 4-cycle. It was proved earlier that r k (C 4 ) k 2 &k+2 for k&1 being a prime power. In this note we establish r k (C 4 ) k 2 +2 for k being