## Abstract For every __r__‐graph __G__ let π(__G__) be the minimal real number ϵ such that for every ϵ < 0 and __n__ ϵ __n__~0~(λ, __G__) every __R__‐graph __H__ with __n__ vertices and more than (π + ϵ)(nr) edges contains a copy of __G__. The real number λ(__G__) is defined in the same way, addin
On several variations of the turan and ramsey numbers
✍ Scribed by Yair Caro
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 424 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
## Abstract For each __n__ and __k__, we examine bounds on the largest number __m__ so that for any __k__‐coloring of the edges of __K~n~__ there exists a copy of __K~m~__ whose edges receive at most __k−__1 colors. We show that for $k \ge \sqrt{n}\;+\,\Omega(n^{1/3})$, the largest value of __m__ i
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.
The Ramsey numbers M,,, n,P,, ..., n,P,), p > 2, are calculated. ## 1. Introduction One class of generalized Ramsey numbers that are known exactly are those for the graphs nP2 which consist of n disjoint paths of length 2; E. J. Cockayne and the author proved in 111 that d r(nlp2, ..., n d P 2 ) =
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