A Characterization of Substar Graphs

TL;DR

This paper characterizes substar graphs through minimal forbidden induced subgraphs, correcting previous inaccuracies and providing a clearer understanding of their structure within intersection graph theory.

Contribution

It offers a corrected and complete characterization of substar graphs by identifying their minimal forbidden induced subgraphs, improving upon prior results.

Findings

Provides a corrected list of minimal forbidden induced subgraphs for substar graphs

Clarifies the structural properties of substar graphs within intersection graph theory

Rectifies a flaw in previous characterization results

Abstract

The intersection graphs of stars in some tree are known as substar graphs. In this paper we give a characterization of substar graphs by the list of minimal forbidden induced subgraphs. This corrects a flaw in the main result of Chang, Jacobson, Monma and West (Subtree and substar intersection numbers, Discrete Appl. Math. 44, 205-220 (1993)) and this leads to a different list of minimal forbidden induced subgraphs.