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Sur Les Partitions en Chaînes du Graphe Divisoriel

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Abstract

On path partitions of the divisor graph. Let D(x) be the graph with vertices {1, 2, ..., ⌊x⌋} whose edges come from the division relation, and let D(x, y) be the subgraph restricted to the integers with prime factors less than or equal to y. We give sufficient conditions on x and y for the graph D(x, y) to be Hamiltonian. We deduce an asymptotic formula for the number of paths in D(x) needed to partition the set of vertices {1, 2, ..., ⌊x⌋}.

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Authors and Affiliations

  1. Université Bordeaux I, UMR 5251, 351 cours de la Libération, F-33 405, Talence cedex, France

    Arnaud Chadozeau

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  1. Arnaud Chadozeau
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Correspondence to Arnaud Chadozeau.

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Communicated by András Sárközy

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Chadozeau, A. Sur Les Partitions en Chaînes du Graphe Divisoriel. Period Math Hung 56, 227–239 (2008). https://doi.org/10.1007/s10998-008-6227-3

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  • DOI: https://doi.org/10.1007/s10998-008-6227-3

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