Mock Threshold Graphs
Richard Behr, Vaidy Sivaraman, and Thomas Zaslavsky

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
