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arXiv · 2203.07686

On Comparable Box Dimension

Zdenek Dvorák·Daniel Goncalves·Abhiruk Lahiri·Jane Tan·Torsten Ueckerdt
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Abstract

Two boxes in $\mathbb{R}^d$ are comparable if one of them is a subset of a translation of the other one. The comparable box dimension of a graph $G$ is the minimum integer $d$ such that $G$ can be represented as a touching graph of comparable axis-aligned boxes in $\mathbb{R}^d$. We show that proper minor-closed classes have bounded comparable box dimensions and explore further properties of this notion.

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Zdenek Dvorák, Daniel Goncalves, Abhiruk Lahiri, Jane Tan, Torsten Ueckerdt. 2022-03-15. On Comparable Box Dimension. https://arxiv.org/abs/2203.07686

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