Avoiding long Berge cycles II, exact bounds for all n

2018/07/16 by Zoltán Füredi, Furedi, Zoltan, Alexandr Kostochka +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1807.06119

openalex publication_date 2018/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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≥ r+3. In this paper we determine EG_r(n,k) and describe the extremal hypergraphs for all n when k≥ r+4.

Citations

• A variation of a theorem by Pósa
• Avoiding long Berge cycles
• On r-uniform hypergraphs with circumference less than r

Related

• On 2-connected hypergraphs with no long cycles
• On r-uniform hypergraphs with circumference less than r
• Avoiding long Berge cycles, the missing cases k=r+1 and k = r+2
• Hypergraphs with few Berge paths of fixed length between vertices
• On 3-uniform hypergraphs avoiding a cycle of length four