An improved quasi-isometry between graphs of bounded cliquewidth and graphs of bounded treewidth
Abstract
Cliquewidth is a dense analogue of treewidth. It can be deduced from recent results by Hickingbotham [arXiv:2501.10840] and Nguyen, Scott, and Seymour [arXiv:2501.09839] that graphs of bounded cliquewidth are quasi-isometric to graphs of bounded treewidth. We improve on this by showing that graphs of cliquewidth admit a partition with `local, but dense' parts whose quotient has treewidth . Specifically, each part is contained within the closed neighbourhood of some vertex. We use this to construct a -quasi-isometry between graphs of cliquewidth and graphs of treewidth . This is an improvement in both the quasi-isometry parameter and the treewidth. We also show that the bound on the treewidth is tight up to an additive constant.
Cite
@article{arxiv.2505.09834,
title = {An improved quasi-isometry between graphs of bounded cliquewidth and graphs of bounded treewidth},
author = {Marc Distel},
journal= {arXiv preprint arXiv:2505.09834},
year = {2025}
}
Comments
v2: Upon receiving feedback that the titular result was implicit in other recent results, revised the paper to instead focus on the improvement other existing results. Added a section on lower bounds to supplement this