On Hamiltonian Berge cycles in 3-uniform hypergraphs

2019/01/18 by Linyuan Lü, Zhiyu Wang, Lu, Linyuan +1 · 2 citations
Engineering · Mathematics · #05C35 #05C65 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1901.06042

openalex publication_date 2019/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a set R, a hypergraph is R-uniform if the size of every hyperedge belongs to R. A hypergraph H is called covering if every vertex pair is contained in some hyperedge in H. In this note, we show that every covering [3]-uniform hypergraph on n≥ 6 vertices contains a Berge cycle C_s for any 3≤ s≤ n. As an application, we determine the maximum Lagrangian of k-uniform Berge-C_t-free hypergraphs and Berge-P_t-free hypergraphs.

Citations

• Some Theorems on Abstract Graphs
• On r-uniform hypergraphs with circumference less than r
• A Rainbow Dirac's Theorem

Cited by

• On the cover Turán number of Berge hypergraphs
• On the cover Ramsey number of Berge hypergraphs

Related

• Spectral radius and Hamiltonicity of uniform hypergraphs
• On 3-uniform hypergraphs without a cycle of a given length
• Avoiding long Berge cycles, the missing cases k=r+1 and k = r+2
• Pósa-type results for Berge-hypergraphs
• On r-uniform linear hypergraphs with no Berge-K_2,t