All Random Solved Random Open
Let $R(G;k)$ denote the minimal $m$ such that if the edges of $K_m$ are $k$-coloured then there is a monochromatic copy of $G$. Is it true that \[R(T;k)=kn+O(1)\] for any tree $T$ on $n$ vertices?
A problem of Erdős and Graham. Implied by [548].

See also the entry in the graphs problem collection.