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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)) .
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Preprints, Working Papers, ...
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Contributor : Paul Melotti Connect in order to contact the contributor
Submitted on : Tuesday, July 24, 2018 - 11:23:11 AM
Last modification on : Saturday, December 4, 2021 - 3:58:23 AM
Long-term archiving on: : Thursday, October 25, 2018 - 1:56:31 PM


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  • HAL Id : hal-01848021, version 1


Paul Melotti, Eric Saias. On path partitions of the divisor graph. 2018. ⟨hal-01848021⟩



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