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arXiv · 2001.05631

Tur\'an numbers for hypergraph star forests

Omid Khormali·Cory Palmer
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Abstract

Fix a graph $F$. We say that a graph is {\it $F$-free} if it does not contain $F$ as a subgraph. The {\it Tur\'an number} of $F$, denoted $\mathrm{ex}(n,F)$, is the maximum number of edges possible in an $n$-vertex $F$-free graph. The study of Tur\'an numbers is a central problem in graph theory. The goal of this paper is to generalize a theorem of Lidick\'y, Liu and Palmer [{\it Electron.\ J.\ of Combin.}\ {\bf 20} (2016)] that determines $\mathrm{ex}(n,F)$ for $F$ a forest of stars. In particular, we consider generalizations of the problem to three different well-studied hypergraph settings and in each case we prove an asymptotic result for all reasonable parameters defining our "star forests".

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Omid Khormali, Cory Palmer. 2020-01-16. Tur\'an numbers for hypergraph star forests. https://arxiv.org/abs/2001.05631

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