On Comparable Box Dimension

March 15, 2022 · The Ethereal · 🏛 International Symposium on Computational Geometry

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Authors Zdenek Dvorák, Daniel Goncalves, Abhiruk Lahiri, Jane Tan, Torsten Ueckerdt arXiv ID 2203.07686 Category cs.DM: Discrete Mathematics Cross-listed cs.DS, math.CO Citations 15 Venue International Symposium on Computational Geometry Last Checked 2 months ago
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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