## Abstract Let __r__~__k__~(__G__) be the __k__‐color Ramsey number of a graph __G__. It is shown that $r\_{k}(C\_{5})\le \sqrt{18^{k}\,k!}$ for __k__⩾2 and that __r__~__k__~(__C__~2__m__+ 1~)⩽(__c__^__k__^__k__!)^1/__m__^ if the Ramsey graphs of __r__~__k__~(__C__~2__m__+ 1~) are not far away fr
3-colored Ramsey Numbers of Odd Cycles
✍ Scribed by Annette Schelten; Ingo Schiermeyer; Ralph Faudree
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 69 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let __n__≥5 be an arbitrary positive odd integer; then, in any two‐coloring of the edges of the complete 5‐partite graph __K__((__n__−1)/2, (__n__−1)/2, (__n__−1)/2, (__n__−1)/2, 1)
For a graph L and an integer k ≥ 2, R k (L) denotes the smallest integer N for which for any edge-coloring of the complete graph K N by k colors there exists a color i for which the corresponding color class contains L as a subgraph.
For two given graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest integer n such that for any graph G of order n, either G contains G 1 or the complement of G contains G 2 . Let C n denote a cycle of order n and W m a wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro
## 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__