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

Authors:
Colin Cooper;Alan Frieze;Bruce Reed
Affiliations:
Department of Mathematical and Computing Sciences, Goldsmiths College, University of London, New Cross, London SE14 6NW, UK (e-mail: c.cooper@gold.ac.uk);Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213, USA (e-mail: alan@random.math.cmu.edu);Equipe Combinatoire, CNRS, Université e de Paris VI, 4 Place Jussieu, Paris 75005, France (e-mail: reed@ecp6.jussieu.fr)
Venue:
Combinatorics, Probability and Computing
Year:
2002

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Abstract

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