On path partitions of the divisor graph - Archive ouverte HAL Access content directly
Journal Articles Acta Arithmetica Year : 2020

On path partitions of the divisor graph

Abstract

It is known that the longest simple path in the divisor graph that uses integers ≤ N is of length 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)) .
Fichier principal
Vignette du fichier
chaines.pdf (370.02 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01848021 , version 1 (24-07-2018)

Identifiers

Cite

Paul Melotti, Eric Saias. On path partitions of the divisor graph. Acta Arithmetica, 2020, 192 (4), pp.329--339. ⟨10.4064/aa180711-26-4⟩. ⟨hal-01848021⟩
73 View
138 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More