Nika Salia: Inverse Turán problems

For a given graph $H$, the classical Tur\'an number $\ex(K_n,H)$ is defined to be the

maximal number of edges which can be taken in an $H$-free subgraph of the complete

graph $K_n$. 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 $\ex(G,H) \le k$. We resolve a problem of Briggs and Cox in the negative by

showing that the inverse Tur\'an number of $K_{2,t}$ is $\Theta(n^{3/2})$, for all $t \ge 2$.

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