Counting Hamiltonian Cycles in Dirac Hypergraphs

2021/10/29 by Asaf Ferber, Ferber, Asaf, Liam Hardiman +3
Computer Science · Mathematics · #05C07 #05C38 #05C45 #05C65 #05C80 #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.2110.15475

openalex publication_date 2021/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For 0≤ ℓ 1/2 has (asymptotically and up to a subexponential factor) at least as many Hamiltonian ℓ-cycles as in a typical random k-graph with edge-probability δ. This significantly improves a recent result of Glock, Gould, Joos, Kühn, and Osthus, and verifies a conjecture of Ferber, Krivelevich and Sudakov for all values 0≤ ℓ

Citations

• Some Theorems on Abstract Graphs

Related

• Robust Hamiltonicity in families of Dirac graphs
• Dirac's Theorem for hamiltonian Berge cycles in uniform hypergraphs
• On extremal hypergraphs for hamiltonian cycles
• Dirac's theorem for random graphs
• Ore-degree threshold for the square of a Hamiltonian cycle