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

Published 26 Jun 2025 in math.CO | (2506.21756v1)

Abstract: In this paper, we prove that for each $d \ge 3$, 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 $d$ but $d=2$.

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