Abstract:We write finite set systems as uniform hypergraphs. A \emph{$t$-matching} in a $k$-uniform hypergraph is a set of hyperedges any two of which intersect in fewer than $t$ vertices. The maximum size of such a set is the \emph{$t$-matching number} and is denoted by $\nu_t$. We study the maximum number of hyperedges in a $k$-uniform hypergraph on $[n]$ with prescribed $t$-matching number. This gives a hypergraph analogue of the Erdős Matching Conjecture. We also determine the second largest maximal structure with $\nu_t(\mathcal{F})=s$, extending work of Frankl and Kupavskii \cite{frankl2016two}. And, we obtain the extremal $G$-free induced subgraphs of generalized Kneser graph, generalizing Alishahi's results in \cite{alishahi2018extremal}.
From: Mengyu Cao [view email]
[v1]
Mon, 18 Aug 2025 07:23:57 UTC (16 KB)
[v2]
Mon, 13 Jul 2026 03:48:09 UTC (14 KB)
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