Circulant graphs and GCD and LCM of Subsets

Joachim von zur Gathen; Igor E. Shparlinski

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arXiv · 1402.5449

Circulant graphs and GCD and LCM of Subsets

Joachim von zur Gathen·Igor E. Shparlinski

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Abstract

Given two sets $A$ and $B$ of integers, we consider the problem of finding a set $S \subseteq A$ of the smallest possible cardinality such the greatest common divisor of the elements of $S \cup B$ equals that of those of $A \cup B$. The particular cases of $B = \emptyset$ and $\#B = 1$ are of special interest and have some links with graph theory. We also consider the corresponding question for the least common multiple of the elements. We establish NP-completeness and approximation results for these problems by relating them to the Minimum Cover Problem.

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Joachim von zur Gathen, Igor E. Shparlinski. 2014-02-21. Circulant graphs and GCD and LCM of Subsets. https://arxiv.org/abs/1402.5449

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