Posets with cover graph of pathwidth two have bounded dimension

Abstract

Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there exists a constant $d$ such that if $P$ is a poset with cover graph of $P$ of pathwidth at most $2$, then $\dim (P)\le d$. We answer this question in the affirmative by showing that $d=17$ is sufficient. We also show that if $P$ is a poset containing the standard example $S_5$ as a subposet, then the cover graph of $P$ has treewidth at least $3$.

18 pages, 9 figures, accepted for publication in Order

Cited by in corpus (4)

• Minors and dimension
• Dimension and cut vertices: an application of Ramsey theory
• Dimension of posets with planar cover graphs excluding two long incomparable chains
• Sparsity and dimension