, Volume 11, Issue 2, pp 179-199

What we know and what we do not know about Turán numbers

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Abstract

The numbers which are traditionally named in honor of Paul Turán were introduced by him as a generalization of a problem he solved in 1941. The general problem of Turán having anextremely simple formulation but beingextremely hard to solve, has become one of the most fascinatingextremal problems in combinatorics. We describe the present situation and list conjectures which are not so hopeless.