On the Dimension of Posets with Cover Graphs of Treewidth 2

On the Dimension of Posets with Cover Graphs of Treewidth

In 1977, Trotter and Moore proved that a poset has dimension at most 3 whenever its cover graph is a forest, or equivalently, has treewidth at most 1. On the other hand, a well-known construction of Kelly shows that there are posets of arbitrarily large dimension whose cover graphs have treewidth 3. In this paper we focus on the boundary case of treewidth 2. It was recently shown that the dimen...

On the Dimension of Posets with Cover Graphs of Treewidth 2

The Dimension of Posets with Planar Cover Graphs

Kelly showed that there exist planar posets of arbitrarily large dimension, and Streib and Trotter showed that the dimension of a poset with a planar cover graph is bounded in terms of its height. Here we continue the study of conditions that bound the dimension of posets with planar cover graphs. We show that if P is a poset with a planar comparability graph, then the dimension of P is at most...

Dimension and Height for Posets with Planar Cover Graphs

We show that for each integer h ≥ 2, there exists a least positive integer ch so that if P is a poset having a planar cover graph and the height of P is h, then the dimension of P is at most ch. Trivially, c1 = 2. Also, Felsner, Li and Trotter showed that c2 exists and is 4, but their proof techniques do not seem to apply when h ≥ 3. We focus on establishing the existence of ch, although we sus...

Cover-Incomparability Graphs of Posets

∗Work supported by the Ministry of Science of Slovenia and by the Ministry of Science and Technology of India under the bilateral India-Slovenia grants BI-IN/06-07-002 and DST/INT/SLOV-P03/05, respectively.