Problem 743

Erdős Problem #743 [status: falsifiable; formalized: no]. Let $T_2,\ldots,T_n$ be a collection of trees such that $T_k$ has $k$ vertices. Can we always write $K_n$ as the edge disjoint union of the $T_k$? Current best: Fishburn [Fi83] proved this for $n\leq 9$. Prize: no. Tags: graph theory.