Parameters Tied to Treewidth

TL;DR

This paper surveys various graph parameters related to treewidth, reviews existing results, improves bounds, simplifies proofs, and establishes tight inequalities, highlighting their fundamental importance in graph theory.

Contribution

It provides a comprehensive survey of parameters tied to treewidth, offers improved bounds, and simplifies proofs, advancing understanding of their relationships.

Findings

Parameters like separation number and tangle number are tightly linked to treewidth.

The paper improves known bounds on these parameters.

It demonstrates that the inequalities relating these parameters are tight.

Abstract

Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This paper surveys several graph parameters tied to treewidth, including separation number, tangle number, well-linked number and Cartesian tree product number. We review many results in the literature showing these parameters are tied to treewidth. In a number of cases we also improve known bounds, provide simpler proofs and show that the inequalities presented are tight.