Book free 3-Uniform Hypergraphs [article]

Debarun Ghosh, Ervin Győri, Judit Nagy-György, Addisu Paulos, Chuanqi Xiao, Oscar Zamora
2021 arXiv   pre-print
One of the first problems in extremal graph theory was the maximum number of edges that a triangle-free graph can have. Mantel solved this, which built the foundations of what we know as extremal graph theory. The natural progression was to ask the maximum number of edges in a k-book free graph. A k-book, denoted by B_k, is k triangles sharing a common edge. In the early 2000s, Győri solved the hypergraph analog of the maximum number of hyperedges in a triangle-free hypergraph. In a hypergraph,
more » ... k-book denotes k Berge triangles sharing a common edge. Let ex_3(n,ℱ) denote the maximum number of hyperedges in a Berge-ℱ-free hypergraph on n vertices. In this paper, we prove ex_3(n,B_k)=n^2/8(1+o(1)).
arXiv:2110.01184v1 fatcat:2wnugg6cqneyvhq6qndhfhnb6u