A note on euclidean Ramsey theory and a construction of Bourgain
β Scribed by N. Alon; Y. Peres
- Publisher
- Akadmiai Kiad
- Year
- 1991
- Tongue
- English
- Weight
- 170 KB
- Volume
- 57
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __r(k__) denote the least integer __n__βsuch that for any graph __G__ on __n__ vertices either __G__ or its complement G contains a complete graph __K__~k~ on __k__ vertices. in this paper, we prove the following lower bound for the Ramsey number __r(k__) by explicit construction: _
## Abstract We prove that there is an absolute constant __C__>0 so that for every natural __n__ there exists a triangleβfree __regular__ graph with no independent set of size at least \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle
Any nonvoid lattice of subspaces from R" is known to be a complete lattice, and hence it has a largest and smallest element. Here we show that for a specific class of subspaces also the converse is true. If this class has a largest and a smallest element, then it is a complete lattice. Within the co