# Ramsey numbers of degenerate graphs

@article{Lee2015RamseyNO, title={Ramsey numbers of degenerate graphs}, author={Choongbum Lee}, journal={arXiv: Combinatorics}, year={2015} }

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 Erdős from 1973.

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