Year: 2021
Type: preprint
Abstract: We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any $γ>0$ and $k\ge3$, we show that asymptotically almost surely, every subgraph of the binomial random $k$-uniform hypergraph $G^{(k)}\big(n,n^{γ-1}\big)$ in which all $(k-1)$-sets are contained in at least $\big(\tfrac12+2γ\big)pn$ edges has a tight Hamilton cycle. This is a cyclic ordering of the $n$ vertices such that each consecutive $k$ vertices forms an edge.
Source: arXiv (Cornell University)
Authors: Allen, Peter, Parczyk, Olaf, Pfenninger, Vincent
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1517153844
OpenAlex ID: W3161878960