Local Ramsey numbers for copies of cycles
β Scribed by Halina Bielak
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 485 KB
- Volume
- 276
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We prove that the 2-local Ramsey number
π SIMILAR VOLUMES
## Abstract In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let __n__β₯5 be an arbitrary positive odd integer; then, in any twoβcoloring of the edges of the complete 5βpartite graph __K__((__n__β1)/2, (__n__β1)/2, (__n__β1)/2, (__n__β1)/2, 1)
## Abstract We determine the maximum number of colors in a coloring of the edges of __K~m,n~__ such that every cycle of length 2__k__ contains at least two edges of the same color. One of our main tools is a result on generalized path covers in balanced bipartite graphs. For positive integers __q__
As usual, for simple graphs G and H, let the Ramsey number r(G,H) be defined as the least number n such that for any graph K of order n, either G is a subgraph of K or H is a subgraph of/(. We shall establish the values of r(aC~,bCs) and r(aCv, bC7) almost precisely (where nG is the graph consisting