Resilience for tight Hamiltonicity
Allen, P.
, Parczyk, O. & Pfenninger, V.
(2024).
Resilience for tight Hamiltonicity.
Combinatorial Theory,
4(1).
https://doi.org/10.5070/C64163846
, Parczyk, O. & Pfenninger, V.
(2024).
Resilience for tight Hamiltonicity.
Combinatorial Theory,
4(1).
https://doi.org/10.5070/C64163846
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 (1/2 + 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.
