Could we realize good bounds on Ramsey theoretic problems using semidefinite programming? Example: Is there a good bound on Ramsey numbers $R(r,s)$ from semidefinite programming?Does number of quantifiers matter in semidefinite programming? In maximizing independence number, we ask  independent set of given size? In Ramsey number we ask  graphs of given size  clique or independent set of given sizes?
Ramsey theory through semidefinite programming
semidefinite programming;ramsey theory