Turán numbers of general star forests in hypergraphs

Abstract

Let $F$ be a family of r-uniform hypergraphs, and let H be an r-uniform hypergraph. Then H is called $F$-free if it does not contain any member of $F$ as a subhypergraph. The Turán number of $F$, denoted by ${\mathrm{ex}}_r(n,F)$, is the maximum number of hyperedges in an $F$-free n-vertex r-uniform hypergraph. Our current results are motivated by earlier results on Turán numbers of star forests and hypergraph star forests. In particular, Lidický et al. (2013) [17] determined the Turán number $\mathrm{ex}(n,F)$ of a star forest F for sufficiently large n. Recently, Khormali and Palmer (2022) [13] generalized the above result to three different well-studied hypergraph settings (the expansions of a graph, linear hypergraphs and Berge hypergraphs), but restricted to the case that all stars in the hypergraph star forests are identical. We further generalize these results to general star forests in hypergraphs.