## 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
On the multi-colored Ramsey numbers of cycles
✍ Scribed by Tomasz Łuczak; Miklós Simonovits; Jozef Skokan
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 82 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
## 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__
## Abstract We introduce several variations of the Turan and Ramsey numbers, including zero‐sum and bounded‐average Ramsey numbers. Some interesting relations between these concepts are presented. In particular, a generalization of the __k__‐local Ramsey numbers is established.
## Abstract Jacobson, Levin, and Scheinerman introduced the fractional Ramsey function __r__~__f__~ (__a__~1~, __a__~2~, …, __a__~__k__~) as an extension of the classical definition for Ramsey numbers. They determined an exact formula for the fractional Ramsey function for the case __k__=2. In this
## On the Number of Discernible On the Number of Discernible Colors Colours I was surprised that, in their study of the number of dis-The authors are grateful to Cal McCamy for his timely cernible colors, Pointer and Attridge 1 missed the early response to their original article. Neither they, nor
## Abstract Given a __list of boxes L__ for a graph __G__ (each vertex is assigned a finite set of colors that we call a box), we denote by __f__(__G, L__) the number of L‐__colorings__ of __G__ (each vertex must be colored wiht a color of its box). In the case where all the boxes are identical and