A graph class G has linear growth if, for each graph G∈G and every positive integer r, every subgraph of G with radius at most r contains O(r) vertices. In this paper, we show that every graph class with linear growth has bounded treewidth.
@article{arxiv.2210.13720,
title = {Graphs of Linear Growth have Bounded Treewidth},
author = {Rutger Campbell and Marc Distel and J. Pascal Gollin and Daniel J. Harvey and Kevin Hendrey and Robert Hickingbotham and Bojan Mohar and David R. Wood},
journal= {arXiv preprint arXiv:2210.13720},
year = {2022}
}