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)=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.
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Biró, C., Keller, M.T. & Young, S.J. Posets with Cover Graph of Pathwidth two have Bounded Dimension. Order 33, 195–212 (2016). https://doi.org/10.1007/s11083-015-9359-7
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DOI: https://doi.org/10.1007/s11083-015-9359-7