I try to find a counterexample for $R(4,4)\neq 8$. (R is the Ramsey-number).
I drew a graph with 8 vedges and I coloured all edges $(v_i,v_j)$ with $i-j =\pm 2,4,6$ in the same colour (for example in red). But then I'll find a $K_4$ with $(v_1,v_3,v_5,v_7)$, which is definitely not a counterexample.
Perhaps someone can help me out here? Thanks in advance.
A simple way to see that $R(4,4) > 9$ is to take three disconnected copies of $K_3$:s. Of course this is very far from being optimal, since the true value is $R(4,4)=18$.