Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

2010/03/30 by Alan Frieze, Frieze, Alan · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #RNA Research and Splicing

paper · pdf · doi:10.48550/arxiv.1003.5817

openalex publication_date 2010/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the random hypergraph H=H(n,p;3) each possible triple appears independently with probability p. A loose Hamilton cycle can be described as a sequence of edges x_i,y_i,x_i+1\ for i=1,2,...,n/2. We prove that there exists an absolute constant K>0 such that if p>Klog n/n² then lim_{n->oo 4 |n}Pr(H(n,p;3) contains a loose Hamilton cycle)=1.

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