MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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