## Abstract This paper is a survey of the methods used for determining exact values and bounds for the classical Ramsey numbers in the case that the sets being colored are two‐element sets. Results concerning the asymptotic behavior of the Ramsey functions __R__(__k,l__) and __R~m~__(__k__) are als
A variant of the classical Ramsey problem
✍ Scribed by Paul Erdős; András Gyárfás
- Publisher
- Springer-Verlag
- Year
- 1997
- Tongue
- English
- Weight
- 478 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
📜 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
## Abstract We consider the following question: how large does __n__ have to be to guarantee that in any two‐coloring of the edges of the complete graph __K__~__n,n__~ there is a monochromatic __K__~__k,k__~? In the late 1970s, Irving showed that it was sufficient, for __k__ large, that __n__ ≥ 2^_