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arXiv · 2502.01631

Minimum degree edge-disjoint Hamilton cycles in random directed graphs

Asaf Ferber·Adva Mond
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Abstract

In this paper we consider the problem of finding ``as many edge-disjoint Hamilton cycles as possible'' in the binomial random digraph $D_{n,p}$. We show that a typical $D_{n,p}$ contains precisely the minimum between the minimum out- and in-degrees many edge-disjoint Hamilton cycles, given that $p\geq \log^{15} n/n$, which is optimal up to a factor of poly$\log n$. Our proof provides a randomized algorithm to generate the cycles and uses a novel idea of generating $D_{n,p}$ in a sophisticated way that enables us to control some key properties, and on an ``online sprinkling'' idea as was introduced by Ferber and Vu.

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Asaf Ferber, Adva Mond. 2025-02-03. Minimum degree edge-disjoint Hamilton cycles in random directed graphs. https://arxiv.org/abs/2502.01631

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