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- W4288595296 abstract "For a graph $F$, we say a hypergraph is a Berge-$F$ if it can be obtained from $F$ by replacing each edge of $F$ with a hyperedge containing it. A hypergraph is Berge-$F$-free if it does not contain a subhypergraph that is a Berge-$F$. The weight of a non-uniform hypergraph $mathcal{H}$ is the quantity $sum_{h in E(mathcal{H})} |h|$. Suppose $mathcal{H}$ is a Berge-$F$-free hypergraph on $n$ vertices. In this short note, we prove that as long as every edge of $mathcal{H}$ has size at least the Ramsey number of $F$ and at most $o(n)$, the weight of $mathcal{H}$ is $o(n^2)$. This result is best possible in some sense. Along the way, we study other weight functions, and strengthen results of Gerbner and Palmer; and Gr'osz, Methuku and Tompkins." @default.
- W4288595296 created "2022-07-29" @default.
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- W4288595296 date "2019-02-09" @default.
- W4288595296 modified "2023-09-23" @default.
- W4288595296 title "On the weight of Berge-$F$-free hypergraphs" @default.
- W4288595296 doi "https://doi.org/10.48550/arxiv.1902.03398" @default.
- W4288595296 hasPublicationYear "2019" @default.
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