Rendiconti del Circolo Matematico di Palermo

, Volume 52, Issue 3, pp 481–488 | Cite as

Etude Du Graphe Divisoriel 3

  • Eric Saias


LetF(N) be the least cardinal number of the number of elements of a partition of {1, 2, …,N} into simple paths of its divisorial graph. We show thatN/6≤F(N)<N/4, the lower bound being valid for allN≥1, and the upper bound forN large enough.


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    Erdös P., Saias E.,Sur le graphe divisoriel, Acta Arith.,73 (1995), 189–198.zbMATHMathSciNetGoogle Scholar
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    Pomerance C.,On the longest path in the divisor graph, Cong. Numer.,40 (1983), 291–304.MathSciNetGoogle Scholar
  3. [3]
    Saias E.,Applications des entiers à diviseurs denses, Acta Arith.,83 (1998), 225–240.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • Eric Saias
    • 1
  1. 1.Laboratoire de Probabilités et modèles aléatoiresUniversité Paris 6Paris Cedex 05France

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