2018/02/13 by Jie Han, Yi Zhao, Han, Jie +1 · 2 citations
Mathematics · #Limits and Structures in Graph Theory #Graph theory and applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1802.04586
For integers k≥ 3 and 1≤ ℓ≤ k-1, we prove that for any α>0, there exist ε>0 and C>0 such that for sufficiently large n∈ (k-ℓ)ℕ, the union of a k-uniform hypergraph with minimum vertex degree αnk-1 and a binomial random k-uniform hypergraph \mathbbG(k)(n,p) with p≥ n-(k-ℓ)-ε for ℓ≥ 2 and p≥ C n-(k-1) for ℓ=1 on the same vertex set contains a Hamiltonian ℓ-cycle with high probability. Our result is best possible up to the values of ε and C and answers a question of Krivelevich, Kwan and Sudakov.