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 a closed neighbourhood of some vertex. We use this to construct a 3‐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.
Marc Distel (Wed,) studied this question.