Erdős–Sós conjecture for trees

Let $T$ be a tree on $t$ vertices. For a graph $G$, write $e(G)$ for its number of edges, and call $G$ $T$-free if it contains no subgraph isomorphic to $T$. Erdős–Sós conjecture. If $T$ is a tree on $t$ vertices, then every $T$-free graph $G$ on $N$ vertices satisfies

$$e(G)\leq \frac{t-2}{2}N.$$

This is the classical linear extremal conjecture for trees, introduced by Erdős. The paper studies its restriction to bipartite host graphs; the general conjecture is presented here without a supplied resolution status.