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Journal Articles Acta Arithmetica Year : 2020

On path partitions of the divisor graph


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



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⟩
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