Hamilton Cycles in Random Lifts of Directed Graphs

Prasad Chebolu, Alan Frieze
2008 SIAM Journal on Discrete Mathematics  
An n-lift of a digraph K, is a digraph with vertex set V (K) × [n] and for each directed edge (i, j) ∈ E(K) there is a perfect matching between fibers {i} × [n] and {j} × [n], with edges directed from fiber i to fiber j. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that if h is sufficiently large then a random n-lift of the complete digraph K h is hamiltonian whp.
doi:10.1137/060670808 fatcat:z5zix6s7vrh6tfl4qbqpzavb6y