A lower bound for the number of vertices of some Ramsey graphs - Nenov, Nedjalko (Ann. Sofia Univ. Fac. Math. and Inf., 1994)
A subset v_1,..v_p of vertices of graph is called da p-clique if any two of them are adjacent. The graph G is called a (p_1,..,p_s)-Ramsey graph, for some set of integers p_1,...p_s if for every colouring of the edges of G there exist an i,1≤ i ≤ s, such that G contains monochromatic p_i-clique of the i-colour. The symbol R(p_1,..p_s) denotes the minimal natural number n such that the complete graph with n vertices is (p_1,..,p_s)-Ramsey graph and the symbol N(R(p_1,...,p_s))-the minimal natural number n such that there exists a (p_1,..,p_s)-Ramsey graph with n vertices and without R(p_1,..,p_s)-clique. In this paper it is proved a lowe bound for the numbers N(R(p_1,..p_s))