3 problems

Bukh–Conlon conjecture. For any balanced rooted tree $(T,R)$ and any natural number $\ell$, we have

For a graph $H$, let $\mathrm{ex}(n,H)$ denote the maximum number of edges in an $n$-vertex graph containing no copy of $H$. Erdős–Simonovits rational exponents conjecture. For eve…

For positive integers $n,s$, let $K_{s,s}$) be the complete bipartite graph with $s$ vertices in each part. For a bipartite graph $H$, let $\mathrm{ex}^*(n,H,s)$ be the maximum num…