The threshold for loose Hamilton cycles in random hypergraph

2025/03/07 by Frieze, Alan, Perez-Gimenez, Xavier · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.05121

Abstract

We show that w.h.p. the random r-uniform hypergraph H_n,m contains a loose Hamilton cycle, provided r≥ 3 and m≥ ((1+ε)nlog n)/(r), where ε is an arbitrary positive constant. This is asymptotically best possible, as if m≤ ((1-ε)nlog n)/(r) then w.h.p. H_n,m contains isolated vertices.

Cited by

• Berge Hamilton cycles in a random sparsification of dense hypergraphs
• Sandwiching between random regular graphs and Erdős-Rényi graphs: configuration model and unions of perfect matchings

Related

• A threshold result for loose Hamiltonicity in random regular uniform hypergraphs
• Loose Hamilton Cycles in Random Uniform Hypergraphs
• Resilience for Loose Hamilton Cycles
• Loose Hamilton Cycles in Random 3-Uniform Hypergraphs
• Tight Hamilton Cycles in Random Uniform Hypergraphs