Obstructions for linear rankwidth at most 1

TL;DR

This paper characterizes graphs with linear rankwidth at most 1 using minimal excluded vertex-minors, providing a structural understanding of these graphs.

Contribution

It offers a new characterization of graphs with linear rankwidth at most 1 through minimal excluded vertex-minors, advancing structural graph theory.

Findings

Identifies minimal excluded vertex-minors for linear rankwidth at most 1

Provides a structural characterization of these graphs

Enhances understanding of graph width parameters

Abstract

We provide a characterization of graphs of linear rankwidth at most 1 by minimal excluded vertex-minors.