Complementary Ramsey numbers and Ramsey graphs
  In this paper, we consider a variant of Ramsey numbers which we call complementary Ramsey numbers $\bar{R}(m,t,s)$. We first establish their connections to pairs of Ramsey $(s,t)$-graphs. Using the classification of Ramsey $(s,t)$-graphs for small $s,t$, we determine the complementary Ramsey numbers $\bar{R}(m,t,s)$ for $(s,t)=(4,4)$ and $(3,6)$. 
Akihiro Munemasa and Masashi Shinohara
math.CO