Inverse Turán problems
Venue: Rényi Institue, Big hall.
For a given graph H, the classical Tur\'an number Undefined control sequence \ex is defined to be the
maximal number of edges which can be taken in an H-free subgraph of the complete
graph Kn. Briggs and Cox introduced a dual version of this problem whereby one
maximizes for a given number k, the number of edges in a ground graph G for
which Undefined control sequence \ex. We resolve a problem of Briggs and Cox in the negative by
showing that the inverse Tur\'an number of K2,t is Θ(n3/2), for all t≥2.
We also obtain improved bounds on the inverse Tur\'an number of even cycles and paths.
Joint with Ervin Győri, Nathan Lemons, Casey Tompkins, Oscar Zamora