On the existence of Hamiltonian cycles in a class of random graphs

A digraph with n vertices and fixed outdegree m is generated randomly so that each such digraph is equally likely to be chosen. We consider the probability of the existence of a Hamiltonian cycle in the graph obtained by ignoring arc orientation. We show that there exists m (=<23) such that a Hamiltonian cycle exists with probability tending to 1 as n tends to infinity.

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