Abstract
Fix a graph F. We say that a graph is F-free if it does not contain F as a subhypergraph. The Turán number of F, denoted ex(n,F), is the maximum number of edges possible in an n-vertex F-free graph. The study of Turán numbers is a central problem in graph theory. The goal of this paper is to generalize a theorem of Lidický, Liu and Palmer [Electron. J. of Combin 20 (2016)] that determines 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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