Hamilton Cycles in Random Lifts of Directed Graphs

Abstract

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 ~ Kh is hamiltonian whp.

DOI: 10.1137/060670808

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@article{Chebolu2008HamiltonCI, title={Hamilton Cycles in Random Lifts of Directed Graphs}, author={Prasad Chebolu and Alan M. Frieze}, journal={SIAM J. Discrete Math.}, year={2008}, volume={22}, pages={520-540} }