Monday, February 8, ****5pm ET**** (10pm GMT, 11am Tue NZDT)
David Wood, Monash University
Hypergraph Colouring via Rosenfeld Counting
The Lovász Local Lemma is a powerful probabilistic technique for proving the existence of combinatorial objects. It is especially useful for colouring graphs and hypergraphs with bounded maximum degree. This talk describes a general theorem for colouring hypergraphs that in many instances matches or slightly improves upon the bounds obtained using the Lovász Local Lemma. Moreover, the theorem shows that there are exponentially many colourings. The elementary and self-contained proof is inspired by a recent result for nonrepetitive colourings by Rosenfeld . We apply our general theorem in the setting of proper hypergraph colouring, proper graph colouring, independent transversals, star colouring, nonrepetitive colouring, frugal colouring, Ramsey number lower bounds, and for k-SAT. This is joint work with Ian Wanless [arXiv:2008.00775].