Linear clique-width and modular decomposition
Combinatorics
2026-02-26 v1
Abstract
A hereditary class of graphs has bounded clique-width if and only if its prime members do, but this lifting property fails for linear clique-width. We prove that a hereditary class has bounded linear clique-width if and only if its prime members do and it contains neither all quasi-threshold graphs nor all complements of quasi-threshold graphs. This generalizes a result of Brignall, Korpelainen, and Vatter, who established the result for cographs.
Keywords
Cite
@article{arxiv.2602.22089,
title = {Linear clique-width and modular decomposition},
author = {Robert Brignall and Michal Opler and Vincent Vatter},
journal= {arXiv preprint arXiv:2602.22089},
year = {2026}
}