English

Hamilton cycles in 3-out

Combinatorics 2020-08-28 v2 Probability

Abstract

Let G_{\rm 3-out} denote the random graph on vertex set [n] in which each vertex chooses 3 neighbors uniformly at random. Note that G_{\rm 3-out} has minimum degree 3 and average degree 6. We prove that the probability that G_{\rm 3-out} is Hamiltonian goes to 1 as n tends to infinity.

Keywords

Cite

@article{arxiv.0904.0431,
  title  = {Hamilton cycles in 3-out},
  author = {Tom Bohman and Alan Frieze},
  journal= {arXiv preprint arXiv:0904.0431},
  year   = {2020}
}

Comments

We removed an annoying typo in equation (17)

R2 v1 2026-06-21T12:47:37.424Z