Ramsey numbers of degenerate graphs

  title={Ramsey numbers of degenerate graphs},
  author={Choongbum Lee},
  journal={arXiv: Combinatorics},
  • Choongbum Lee
  • Published 18 May 2015
  • Mathematics
  • arXiv: Combinatorics
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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