Forbidden induced subgraphs of double-split graphs

TL;DR

This paper characterizes the forbidden induced subgraphs of double-split graphs, a class related to perfect graphs, by identifying 44 specific graphs that cannot appear as induced subgraphs.

Contribution

It provides the first forbidden induced subgraph characterization for double-split graphs, completing part of the understanding of perfect graph classes.

Findings

Identified 44 forbidden induced subgraphs for doubled graphs.

Extended the understanding of perfect graph subclasses.

Provided tools for recognizing double-split graphs.

Abstract

In the course of proving the strong perfect graph theorem, Chudnovsky, Robertson, Seymour, and Thomas showed that every perfect graph either belongs to one of five basic classes or admits one of several decompositions. Four of the basic classes are closed under taking induced subgraphs (and have known forbidden subgraph characterizations), while the fifth one, consisting of double-split graphs, is not. A graph is doubled if it is an induced subgraph of a double-split graph. We find the forbidden induced subgraph characterization of doubled graphs; it contains 44 graphs.