Hamilton cycles in regular graphs perturbed by a random 2-factor

Cicely; Henderson; Sean Longbrake; Dingjia Mao; Patryk Morawski

Hamilton cycles in regular graphs perturbed by a random 2-factor

Combinatorics 2025-08-26 v2

Authors: Cicely , Henderson , Sean Longbrake , Dingjia Mao , Patryk Morawski

Abstract

In this paper, we prove that for each $d \geq 2$ , the union of a $d$ -regular graph with a uniformly random $2$ -factor on the same vertex set is Hamiltonian with high probability. This resolves a conjecture by Dragani\'c and Keevash for all values of $d$ .

Keywords

hamilton cycles random graphs periodic orbits in hamiltonian systems

Cite

@article{arxiv.2506.21756,
  title  = {Hamilton cycles in regular graphs perturbed by a random 2-factor},
  author = {Cicely and Henderson and Sean Longbrake and Dingjia Mao and Patryk Morawski},
  journal= {arXiv preprint arXiv:2506.21756},
  year   = {2025}
}

Comments

17 pages, complete the case of $d=2$

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