# Tag Info

One goal of Ramsey theory is to calculate Ramsey numbers $R(r, s)$: For any positive integers $r$ and $s$, there is a smallest positive integer $R(r, s)$ such that any two-colouring of the edges of a complete graph on $R(r, s)$ vertices has a complete subgraph on $r$ which is entirely of the first colour, or a complete subgraph on $s$ vertices which is entirely of the second colour. The Theorem on Friends and Strangers shows that $R(3, 3) \leq 6$ (in fact, $R(3, 3) = 6$).
The notion of Ramsey numbers can be generalised by considering $k$-coloured graphs.