Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least k
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 [(k - 1)/2] edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size [n/2]. We prove that, for k ≥ 3, there is a constant Ck such that if 2m ≥ Ckn then Ak occurs in Gn,m,k with probability tending to 1 as n → ∞. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 42-59, 2000.
Journal of Graph Theory
Bollobás, B., Cooper, C., Fenner, T., & Frieze, A. (2000). Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least k. Journal of Graph Theory, 34 (1), 42-59. https://doi.org/10.1002/(SICI)1097-0118(200005)34:1<42::AID-JGT5>3.0.CO;2-H