Semidefinite Programming and Ramsey Numbers

Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method was developed find asymptotic results for very large graphs, so it seems that the not suitable finding numbers. But this intuition wrong, and we will develop technique do just in paper. We new upper bounds many graph hypergraph As result, prove values $R(K_4^-,K_4^-,K_4^-)=28$, $R(K_8,C_5)= 29$, $R(K_9,C_6)= 41$, $R(Q_3,Q_3)=13$, $R(K_{3,5},K_{1,6})=17$, $R(C_3, C_5, C_5)= 17$, $R(K_4^-,K_5^-;3)= 12$. hope be adapted address other questions smaller graphs with method.