Berge cycles in non-uniform hypergraphs

2020/02/05 by Zoltán Füredi, Furedi, Zoltan, Alexandr Kostochka +3 · 3 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2002.01597

openalex publication_date 2020/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider two extremal problems for set systems without long Berge cycles. First we give Dirac-type minimum degree conditions that force long Berge cycles. Next we give an upper bound for the number of hyperedges in a hypergraph with bounded circumference. Both results are best possible in infinitely many cases.

Citations

• A Rainbow Dirac's Theorem

Cited by

• An Ore-type theorem for [3]-graphs
• Berge k-Factors of Regular Hypergraphs
• Pancyclicity in hypergraphs with large uniformity

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• Hypergraphs with few Berge paths of fixed length between vertices
• Pósa-type results for Berge-hypergraphs
• A note on the Turán number of a Berge odd cycle
• On 3-uniform hypergraphs without a cycle of a given length