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arxiv: 1812.10737 · v2 · pith:CIICNFYDnew · submitted 2018-12-27 · 🧮 math.CO

The Structure of Hypergraphs without long Berge cycles

classification 🧮 math.CO
keywords hypergraphsbergecyclesdeterminegivingstructurewhenaffirmative
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We study the structure of $r$-uniform hypergraphs containing no Berge cycles of length at least $k$ for $k \leq r$, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when $k=r$ and giving a a simple solution to a recent result of Kostochka-Luo when $k < r$.

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