Monday March 5th at 4.30pm

(k-1)-sets of vertices is an independent set? When k=2 we are just asking for the maximum number of edges in a triangle-free graph on n vertices.

This was answered by Mantel in 1907 and is the first result of extremal graph theory. The case k=3 was answered in 2005 by Furedi,

Pikhurko and Simonovits. I will present a proof of the next case k=4. This is joint work with Zoltan Furedi and Oleg Pikhurko.