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].