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arXiv · 2506.21756

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

Cicely·Henderson·Sean Longbrake·Dingjia Mao·Patryk Morawski
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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 Draganić and Keevash for all values of $d$.

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Cicely, Henderson, Sean Longbrake, Dingjia Mao, Patryk Morawski. 2025-08-25. Hamilton cycles in regular graphs perturbed by a random 2-factor. https://arxiv.org/abs/2506.21756

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