Problem 557

Erdős Problem #557: declared status 'open'. Formalized: no. 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$$R(T;k)\leq kn+O(1)$$for any tree $T$ on $n$ vertices? Prize: no. Tags: graph theory, ramsey theory.