A class of Ramsey-extremal hypergraphs

In ۱۹۹۱‎, ‎McKay and Radziszowski proved that‎, ‎however each ۳-subset of a ۱۳-set is assigned one of two colours‎, ‎there is some ۴-subset whose four ۳-subsets have the same colour‎. ‎More than ۲۵ 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 ۳-subsets of a ۱۲-set and list some of their properties‎. ‎We also provide an answer to a question of Dudek‎, ‎La Fleur‎, ‎Mubayi and R\"odl about the size-Ramsey numbers of hypergraphs‎.

کلیدواژه ها:

hypergraph ، Ramsey number ، size-Ramsey number