# Ramsey number inequality problem

1. Jul 5, 2011

### Bingk

Prove that
$R(p,q) \leq \left(\stackrel{p+q-2}{p-1}\right)$
where $p$ and $q$ are positive integers

I'm supposed to use induction on the inequality $R(p,q) \leq R(p-1,q) + R(p,q-1)$, but I'm having difficulty there.

How do I go about doing this? I can show it's true for $p=q=1$.
But, I can't see how I get the combination in the first inequality from an induction on the second inequality (which doesn't contain a combination) ...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 5, 2011

### kompik

Last edited by a moderator: Apr 26, 2017