Book free $3$-Uniform Hypergraphs
Debarun Ghosh, Ervin Gy\H{o}ri, Judit Nagy-Gy\"orgy, Addisu Paulos,, Chuanqi Xiao, Oscar Zamora

TL;DR
This paper establishes an upper bound on the number of hyperedges in large 3-uniform hypergraphs that do not contain a specific structure called a $k$-book, extending understanding of hypergraph extremal problems.
Contribution
It proves a tight asymptotic upper bound on the maximum number of hyperedges in $k$-book-free 3-uniform hypergraphs, a new result in hypergraph extremal theory.
Findings
Maximum hyperedges is at most n^2/8 (1+o(1)) for large n.
Introduces bounds for $k$-book-free 3-uniform hypergraphs.
Advances extremal combinatorics in hypergraph structures.
Abstract
A -book in a hypergraph consists of Berge triangles sharing a common edge. In this paper we prove that the number of the hyperedges in a -book-free 3-uniform hypergraph on vertices is at most .
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Taxonomy
TopicsLimits and Structures in Graph Theory · graph theory and CDMA systems · Advanced Graph Theory Research
