Let R(s,s,s) be the smallest integer n such that every 3-coloring of the edges of Kn contains a monochromatic Ks.
1) show R(s,s,s) ≤ 27^s
2) calculate an exponential lower bound for R(s,s,s), which grows exponentially with s.
For 1) I derived that $R(s,s,s) < R (s,R(s,s)) = R(s, \binom{2s-2}{s-1})$ I dont really know how to derive the 27^s result.
for 2) any hint would be appreciated.