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On Comparable Box Dimension

Publication at Faculty of Mathematics and Physics |
2022

Abstract

Two boxes in Rd 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 Rd.

We show that proper minor-closed classes have bounded comparable box dimension and explore further properties of this notion.