Each 11-vertex graph without 4-cliques has a triangle-free 2-partition of vertices - Nedialkov, Evgeni; Nenov, Nedyalko (Ann. Sofia Univ. Fac. Math. and Inf., 1999)
Let G be a graph, cl(G) denotes the clique number of the graph G. By G → (3,3) we denote that in any 2-partition V_1 V_2 of the set V(G) of his vertices either V_1 or V_2 contains 3-clique (triangle) of the graph G; α = min|V(G)|, G → (3,3) and cl(G) = 4, β = min|V(G)|, G → (3,3) and cl(G) = 3. In the current article, we consider graphs G with the property G → (3,3). As a consequence from proven results it follows that α = 8 and β ≥ 12.