A few remarks on Ramsey--Turán-type problems
Journal of Combinatorial Theory Series B
Extremal Graph Theory
On graphs with small Ramsey numbers
Journal of Graph Theory
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Let F"k denote the family of 2-edge-colored complete graphs on 2k vertices in which one color forms either a clique of order k or two disjoint cliques of order k. Bollobas conjectured that for every @e0 and positive integer k there is n(k,@e) such that every 2-edge-coloring of the complete graph of order n=n(k,@e) which has at least @e(n2) edges in each color contains a member of F"k. This conjecture was proved by Cutler and Montagh, who showed that n(k,@e)