Tree-width and dimension

TL;DR

This paper establishes a relationship between the dimension of finite posets and the tree-width of their cover graphs, extending previous research linking poset dimension and graph planarity.

Contribution

It proves that the dimension of a finite poset is bounded by its height and the tree-width of its cover graph, bridging poset theory and structural graph parameters.

Findings

Dimension is bounded by height and tree-width of cover graph

Extends previous work connecting poset dimension and planarity

Provides new bounds linking poset and graph parameters

Abstract

Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.