Hamilton cycles in quasirandom hypergraphs

2015/02/13 by John Lenz, Lenz, John, Dhruv Mubayi +3 · 2 citations
Engineering · Mathematics · #05C65 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1502.04041

openalex publication_date 2015/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(n^k-1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ-cycle if k-ℓ divides k. The remaining values of ℓ form an interesting open question.

Citations

• Some Theorems on Abstract Graphs

Cited by

• Sharp Diagonal Thresholds for Tight Hamilton Cycles in Uniformly Dense 3-Graphs
• Loose Hamiltonicity

Related

• Hamilton ℓ-cycles in randomly-perturbed hypergraphs
• Decomposing hypergraphs into cycle factors
• Packing tight Hamilton cycles in uniform hypergraphs
• Minimum degree thresholds for Hamilton (ℓ,k-ℓ)-cycles in k-uniform hypergraphs
• Loose Hamiltonicity