Random Regular Graphs of Non-Constant Degree: Connectivity and Hamiltonicity

Let Gr denote a graph chosen uniformly at random from the set of r-regular graphs with vertex set l1,2, …, nr, where 3 l r l c0n for some small constant c0. We prove that, with probability tending to 1 as n → ∞, Gr is r-connected and Hamiltonian.

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