Bounding the Clique-Width of $H$-free Split Graphs

TL;DR

This paper classifies which $H$-free split graphs have bounded clique-width, identifying five new classes and nearly completing the classification for all but two unresolved cases.

Contribution

It introduces five new classes of $H$-free split graphs with bounded clique-width and advances the classification of all such graphs except two remaining cases.

Findings

Identified five new classes of $H$-free split graphs with bounded clique-width.

Provided a near-complete classification of $H$-free split graphs regarding bounded clique-width.

Determined all but two cases for the boundedness of clique-width in $H$-free split graphs.

Abstract

A graph is $H$-free if it has no induced subgraph isomorphic to $H$. We continue a study into the boundedness of clique-width of subclasses of perfect graphs. We identify five new classes of $H$-free split graphs whose clique-width is bounded. Our main result, obtained by combining new and known results, provides a classification of all but two stubborn cases, that is, with two potential exceptions we determine all graphs $H$ for which the class of $H$-free split graphs has bounded clique-width.