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

Abstract

In this paper, we prove that for each $d\ge 2$, 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 Draganić and Keevash for all values of $d$.

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