Induced subgraphs and tree decompositions XVIII. Obstructions to bounded pathwidth

TL;DR

This paper classifies the unavoidable induced subgraphs in graphs with large pathwidth, providing insights into the structure of graphs with high pathwidth.

Contribution

It offers a complete classification of the induced subgraphs that must appear in graphs with large pathwidth, advancing understanding of graph structure.

Findings

Identifies all unavoidable induced subgraphs for high pathwidth graphs

Provides structural characterization of graphs with large pathwidth

Enhances understanding of graph decomposition related to pathwidth

Abstract

The pathwidth of a graph $G$ is the smallest $w\in \mathbb{N}$ such that $G$ can be constructed from a sequence of graphs, each on at most $w+1$ vertices, by gluing them together in a linear fashion. We provide a full classification of the unavoidable induced subgraphs of graphs with large pathwidth.