An exact extremal result for tournaments and 4uniform hypergraphs
Abstract
In this paper, we address the following problem due to Frankl and Füredi (1984). What is the maximum number of hyperedges in an $r$uniform hypergraph with $n$ vertices, such that every set of $r+1$ vertices contains $0$ or exactly $2$ hyperedges? They solved this problem for $r=3$. For $r=4$, a partial solution is given by Gunderson and Semeraro (2017) when $n=q+1$ for some prime power number $q\equiv3\pmod{4} $. Assuming the existence of skewsymmetric conference matrices for every order divisible by $4$, we give a solution for $n\equiv0\pmod{4} $ and for $n\equiv3\pmod{4}$.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.07621
 Bibcode:
 2018arXiv180207621B
 Keywords:

 Mathematics  Combinatorics