Posets with Cover Graph of Pathwidth two have Bounded Dimension
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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)=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 S5 as a subposet, then the cover graph of P has treewidth at least 3.
KeywordsPoset Pathwidth Cover graph Dimension
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