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arXiv · 1807.07783

On path partitions of the divisor graph

Paul Melotti·Eric Saias
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Abstract

It is known that the longest simple path in the divisor graph that uses integers $\leq N$ is of length $\asymp N/\log N$. We study the partitions of $\{1,2,\dots, N\}$ into a minimal number of paths of the divisor graph, and we show that in such a partition, the longest path can have length asymptotically $N^{1-o(1)}$.

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Paul Melotti, Eric Saias. 2018-07-20. On path partitions of the divisor graph. https://arxiv.org/abs/1807.07783

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