On path partitions of the divisor graph
Résumé
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)) .
Domaines
Théorie des nombres [math.NT]| Origine | Fichiers produits par l'(les) auteur(s) |
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