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The ℤ-Divisor Graph on ℚ ∩ [1,7] is Planar and 3-Colorable
Abstract
We prove that a divisor graph on an interval of integers is a planar graph whenever the interval [n,m] satisfies m≤ 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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BibTeX
@misc{walton2026ℤdivisor,
title = {{The $\mathbbZ$-Divisor Graph on $\mathbbQ \cap [1,7]$ is Planar and 3-Colorable}},
author = {Michael D. Walton and Zachary D. Walton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24724},
eprint = {2609.24724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24724},
}
RIS
TY - UNPB
TI - The ℤ-Divisor Graph on ℚ ∩ [1,7] is Planar and 3-Colorable
AU - Michael D. Walton
AU - Zachary D. Walton
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24724
UR - https://arxiv.org/abs/2609.24724
AB - We prove that a divisor graph on an interval of integers is a planar graph whenever the interval [n,m] satisfies m≤ 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.
ER -