Note on a Ramsey-Turán type problem

Solving a problem of Erdös the existence of a graph withn vertices,cn2 edges and withoutK(4) andK(3, 3, 3) is proved. It remains an open question whether all such graphs containK(2, 2, 2).

[1]  P. Erdös,et al.  Graph Theory and Probability , 1959 .

[2]  Béla Bollobás,et al.  On a Ramsey-Turán type problem , 1976, Journal of combinatorial theory. Series B (Print).