Mock Threshold Graphs

TL;DR

Mock threshold graphs extend threshold graphs, maintaining perfection, with characterizations via forbidden subgraphs and special properties like being claw-free or line graphs, along with discussions on algorithms and structural relations.

Contribution

The paper provides a new characterization of mock threshold graphs through forbidden induced subgraphs and explores their properties and algorithmic aspects.

Findings

Characterization of mock threshold graphs by forbidden subgraphs

Identification of conditions for claw-free and line graph subclasses

Discussion on relations with chordality and well-quasi-ordering

Abstract

Mock threshold graphs are a simple generalization of threshold graphs that, like threshold graphs, are perfect graphs. Our main theorem is a characterization of mock threshold graphs by forbidden induced subgraphs. Other theorems characterize mock threshold graphs that are claw-free and that are line graphs. We also discuss relations with chordality and well-quasi-ordering as well as algorithmic aspects.