Is the Ramsey number $R(m + 1, n) \ge R(m, n)$ for all $m, n \ge 2$

Question

Is the Ramsey number $R(m + 1, n) \ge R(m, n)$ for all $m, n \ge 2$.

I'm having trouble proving this inequality. Could anyone offer a hint?

Answer 1

Take the complete graph with $R(m+1, n)$ vertices. What does the definition of $R(m+1, n)$ say about this graph? Is it then not quite clear from the definition of $R$ that this graph has at least $R(m, n)$ vertices?