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MiS Preprint

On Turán numbers for disconnected hypergraphs

Raffaella Mulas and Jiaxi Nie


We introduce the following simpler variant of the Turán problem:
Given integers $n>k>r\geq 2$ and $m\geq 1$, what is the smallest integer $t$ for which there exists an $r$-uniform hypergraph with $n$ vertices, $t$ edges and $m$ connected components such that any $k$-subset of the vertex set contains at least one edge? We prove some general estimates for this quantity and for its limit, normalized by $\binom{n}{r}$, as $n\rightarrow \infty$. Moreover, we give a complete solution of the problem for the particular case when $k=5$, $r=3$ and $m\geq 2$.


Related publications

2023 Repository Open Access
Raffaella Mulas and Jiaxi Nie

On Turán numbers for disconnected hypergraphs

In: Acta mathematica hungarica, 170 (2023) 1, pp. 168-182