POSETS WITH COVER GRAPH OF PATHWIDTH TWO HAVE BOUNDED DIMENSION

Abstract

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. 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. 1.