Order

, Volume 33, Issue 2, pp 195–212 | Cite as

Posets with Cover Graph of Pathwidth two have Bounded Dimension

  • Csaba Biró
  • Mitchel T. Keller
  • Stephen J. Young
Article

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 S5 as a subposet, then the cover graph of P has treewidth at least 3.

Keywords

Poset Pathwidth Cover graph Dimension 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Csaba Biró
    • 1
  • Mitchel T. Keller
    • 2
  • Stephen J. Young
    • 1
  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  2. 2.Department of MathematicsWashington and Lee UniversityLexingtonUSA

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