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arxiv: 1807.06119 · v1 · pith:UMSWYATInew · submitted 2018-07-16 · 🧮 math.CO

Avoiding long Berge cycles II, exact bounds for all n

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keywords bergecyclesexactextremalhypergraphswhenavoidingbounds
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Let $EG_r(n,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph with no Berge cycles of length $k$ or longer. In the first part of this work, we have found exact values of $EG_r(n,k)$ and described the structure of extremal hypergraphs for the case when $k-2$ divides $n-1$ and $k\geq r+3$. In this paper we determine $EG_r(n,k)$ and describe the extremal hypergraphs for all $n$ when $k\geq r+4$.

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