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

COLIN COOPER, ALAN FRIEZE, BRUCE REED

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Source: Crossref

Published: May 1, 2002

DOI: 10.1017/s0963548301005090

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Source abstract

Let G r denote a graph chosen uniformly at random from the set of r -regular graphs with vertex set {1,2, …, n }, where 3 [les ] r [les ] c 0 n for some small constant c 0 . We prove that, with probability tending to 1 as n → ∞, G r is r -connected and Hamiltonian.

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