Tree-width and dimension

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.

Updates on solutions of problems and on bibliography

Cited by in corpus (6)

• Minors and dimension
• Planar posets have dimension at most linear in their height
• Posets with cover graph of pathwidth two have bounded dimension
• Dimension of posets with planar cover graphs excluding two long incomparable chains
• Sparsity and dimension
• Excluding a ladder