Resilience for tight Hamiltonicity [article]

Peter Allen, Olaf Parczyk, Vincent Pfenninger
2021 arXiv   pre-print
We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any γ>0 and k≥3, we show that asymptotically almost surely, every subgraph of the binomial random k-uniform hypergraph G^(k)(n,n^γ-1) in which all (k-1)-sets are contained in at least (12+2γ)pn edges has a tight Hamilton cycle. This is a cyclic ordering of the n vertices such that each consecutive k vertices forms an edge.
arXiv:2105.04513v1 fatcat:y3gyj67jknc4tkkxsxlv3ltkfy