On Comparable Box Dimension

03/15/2022

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by   Zdeněk Dvořák, et al.

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Two boxes in 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 ℝ^d. We show that proper minor-closed classes have bounded comparable box dimensions and explore further properties of this notion.