Hypergraphs of bounded disjointness
Alex Scott, Elizabeth Wilmer

TL;DR
This paper proves a conjecture about the maximum size of certain hypergraphs with bounded disjointness, identifying extremal configurations and advancing understanding of hypergraph intersection properties.
Contribution
It proves a strengthened version of a conjecture on the maximum edges in s-almost intersecting hypergraphs and characterizes extremal graphs.
Findings
Confirmed the conjecture for all relevant parameters.
Identified extremal hypergraph structures.
Provided related results and conjectures.
Abstract
A -uniform hypergraph is -almost intersecting if every edge is disjoint from exactly other edges. Gerbner, Lemons, Palmer, Patk\'os and Sz\'ecsi conjectured that for every , and , every -uniform -almost intersecting hypergraph has at most edges. We prove a strengthened version of this conjecture and determine the extremal graphs. We also give some related results and conjectures.
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