A class of Ramsey-extremal hypergraphs
نویسندگان
1 Dept. of Computer Engg., YMCA University of Science And Technology, Faridabad, HR 121006, India
2 Dept. of Computer Engg., YMCA University of Science And Technology, Faridabad, HR 121006, India
3 Wright State University
doi
10.22108/toc.2017.21468چکیده
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. We also provide an answer to a question of Dudek, La Fleur, Mubayi and R\"odl about the size-Ramsey numbers of hypergraphs.
