# Ramsey number

## Ramsey properties of Cayley graphs ★★★

Author(s): Alon

**Conjecture**There exists a fixed constant so that every abelian group has a subset with so that the Cayley graph has no clique or independent set of size .

Keywords: Cayley graph; Ramsey number

## Diagonal Ramsey numbers ★★★★

Author(s): Erdos

Let denote the diagonal Ramsey number.

**Conjecture**exists.

**Problem**Determine the limit in the above conjecture (assuming it exists).

Keywords: Ramsey number