On Low Tree-Depth Decompositions

TL;DR

This paper surveys the properties and applications of low tree-depth graph decompositions, emphasizing their role in constructing and analyzing complex sparse and dense graph structures.

Contribution

It provides a comprehensive overview of low tree-depth decompositions and their significance in graph theory and structure analysis.

Findings

Low tree-depth graphs facilitate graph decomposition and construction.

These decompositions are crucial in understanding sparse and dense graph classes.

The survey highlights various applications in graph algorithms and structure theory.

Abstract

The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth. In this paper we survey results related to this concept and particularly explain how these graphs are used to decompose and construct more complex graphs and structures. In more technical terms we survey some of the properties and applications of low tree depth decomposition of graphs.