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The Z\mathbb{Z}-Divisor Graph on Q[1,7]\mathbb{Q} \cap [1,7] is Planar and 3-Colorable

Michael D. Walton, Zachary D. Walton

Source record

Source: arXiv

Published: Sep 21, 2026

arXiv: 2609.24724

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Source abstract

We prove that a divisor graph on an interval of integers is a planar graph whenever the interval [n,m][n,m] satisfies m7nm\leq 7n, and that 7 is the greatest such real number for which we can guarantee that the graph is planar. We prove these graphs are 3-colorable.

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