On path partitions of the divisor graph

2018/07/20 by Melotti, Paul, Saias, Eric · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1807.07783

Abstract

It is known that the longest simple path in the divisor graph that uses integers ≤ N is of length \asymp N/log N. We study the partitions of \1,2,…, 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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• On divisibility relation graphs

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