Corpus ID: 234338466

Resilience for tight Hamiltonicity

  title={Resilience for tight Hamiltonicity},
  author={Peter Allen and O. Parczyk and Vincent Pfenninger},
We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any $\gamma>0$ and $k\ge3$, we show that asymptotically almost surely, every subgraph of the binomial random $k$-uniform hypergraph $G^{(k)}\big(n,n^{\gamma-1}\big)$ in which all $(k-1)$-sets are contained in at least $\big(\tfrac12+2\gamma\big)pn$ edges has a tight Hamilton cycle. This is a cyclic ordering of the $n$ vertices such that each consecutive $k$ vertices forms an edge. 

Figures from this paper