  A graph is $d$-degenerate if all its subgraphs have a vertex of degree at
most $d$. We prove that there exists a constant $c$ such that for all natural
numbers $d$ and $r$, every $d$-degenerate graph $H$ of chromatic number $r$
with $|V(H)| \ge 2^{d^22^{cr}}$ has Ramsey number at most $2^{d2^{cr}} |V(H)|$.
This solves a conjecture of Burr and Erd\H{o}s from 1973.
