A class of Ramsey-extremal hypergraphs
Combinatorics
2016-08-30 v1
Abstract
In 1991, McKay and Radziszowski proved that, however each 3-subset of a 13-set is assigned one of two colours, there is some 4-subset whose four 3-subsets have the same colour. More than 25 years later, this remains the only non-trivial classical Ramsey number known for hypergraphs. In this article, we find all the extremal colourings of the 3-subsets of a 12-set and list some of their properties. Using the catalogue, we provide an answer to a question of Dudek, Fleur, Mubayi and R\"odl about the size-Ramsey numbers of hypergraphs.
Keywords
Cite
@article{arxiv.1608.07762,
title = {A class of Ramsey-extremal hypergraphs},
author = {Brendan D. McKay},
journal= {arXiv preprint arXiv:1608.07762},
year = {2016}
}