Linear Clique-Width for Hereditary Classes of Cographs

TL;DR

This paper characterizes when hereditary classes of cographs have bounded linear clique-width, linking it to the exclusion of all quasi-threshold graphs and their complements, with proof techniques inspired by permutation class enumeration.

Contribution

It provides a precise characterization of hereditary cograph classes with bounded linear clique-width, connecting graph structure with permutation class enumeration methods.

Findings

Hereditary cograph classes have bounded linear clique-width iff they exclude all quasi-threshold graphs and their complements.

The proof uses ideas from permutation class enumeration.

The result clarifies the structural conditions for bounded linear clique-width in hereditary cographs.

Abstract

The class of cographs is known to have unbounded linear clique-width. We prove that a hereditary class of cographs has bounded linear clique-width if and only if it does not contain all quasi-threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes.