Sparse String Graphs and Region Intersection Graphs over Minor-Closed Classes have Linear Expansion
Combinatorics
2026-04-10 v1 Discrete Mathematics
Abstract
We prove that sparse string graphs in a fixed surface have linear expansion. We extend this result to the more general setting of sparse region intersection graphs over any proper minor-closed class. The proofs are combinatorial and self-contained, and provide bounds that are within a constant factor of optimal. Applications of our results to graph colouring are presented.
Keywords
Cite
@article{arxiv.2604.07903,
title = {Sparse String Graphs and Region Intersection Graphs over Minor-Closed Classes have Linear Expansion},
author = {Nikolai Karol and David R. Wood},
journal= {arXiv preprint arXiv:2604.07903},
year = {2026}
}