Proper Minor-Closed Classes of Graphs have Assouad-Nagata Dimension 2
Combinatorics
2025-05-16 v3 Metric Geometry
Abstract
Asymptotic dimension and Assouad-Nagata dimension are measures of the large-scale shape of a class of graphs. Bonamy, Bousquet, Esperet, Groenland, Liu, Pirot, and Scott [J. Eur. Math. Society] showed that any proper minor-closed class has asymptotic dimension 2, dropping to 1 only if the treewidth is bounded. We improve this result by showing it also holds for the stricter Assouad-Nagata dimension. We also characterise when subdivision-closed classes of graphs have bounded Assouad-Nagata dimension.
Keywords
Cite
@article{arxiv.2308.10377,
title = {Proper Minor-Closed Classes of Graphs have Assouad-Nagata Dimension 2},
author = {Marc Distel},
journal= {arXiv preprint arXiv:2308.10377},
year = {2025}
}
Comments
v2: Acknowledges an independent proof of the main result by Chun-Hung Liu, available at arXiv:2308.12273. v3: Minor changes, mostly grammar/typo fixes