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arXiv · 2001.01149

The probability of selecting $k$ edge-disjoint Hamilton cycles in the complete graph

Asaf Ferber·Kaarel Haenni·Vishesh Jain
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Abstract

Let $H_1,\dots,H_k$ be Hamilton cycles in $K_n$, chosen independently and uniformly at random. We show, for $k = o(n^{1/100})$, that the probability of $H_1,\dots,H_k$ being edge-disjoint is $(1+o(1))e^{-2\binom{k}{2}}$. This extends a corresponding estimate obtained by Robbins in the case $k=2$.

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Asaf Ferber, Kaarel Haenni, Vishesh Jain. 2020-01-05. The probability of selecting $k$ edge-disjoint Hamilton cycles in the complete graph. https://arxiv.org/abs/2001.01149

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