Hamilton cycles in 3-out

Authors:
Tom Bohman;Alan Frieze
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Venue:
Random Structures & Algorithms
Year:
2009

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Abstract

Let G3-out denote the random graph on vertex set [n] in which each vertex chooses three neighbors uniformly at random. Note that G3-out has minimum degree 3 and average degree 6. We prove that the probability that G3-out is Hamiltonian goes to 1 as n tends to infinity. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009