Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least k

@article{Bollobs2000EdgeDH,
  title={Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least k},
  author={B{\'e}la Bollob{\'a}s and Colin S Cooper and Trevor I. Fenner and Alan M. Frieze},
  journal={Journal of Graph Theory},
  year={2000},
  volume={34},
  pages={42-59}
}
Let Gn,m,k denote the space of simple graphs with n vertices, m edges and minimum degree at least k, each graph G being equiprobable. Let G have property Ak if G contains b(k − 1)/2c edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size bn/2c. For k ≥ 3, Ak occurs in Gn,m,k with probability tending to 1 as n →∞, when 2m ≥ ckn for some suitable constant ck. ∗Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA. †School of… CONTINUE READING