Let be a finite set. A family of subsets of is called a convex geometry with ground set if (1);(2)
whenever; and (3) if and, there is an element such that. As a nonempty family of sets, a …

The dimension of a poset $ P $ is the minimum number of total orders whose intersection is
$ P $. We prove that the dimension of every poset whose comparability graph has maximum …

We prove that posets of bounded height whose cover graphs belong to a fixed class with
bounded expansion have bounded dimension. Bounded expansion, introduced by Nešetřil …

Abstract 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 …

Nowhere dense graph classes provide one of the least restrictive notions of sparsity for
graphs. Several equivalent characterizations of nowhere dense classes have been obtained …

It has been known for 30 years that posets with bounded height and with cover graphs of
bounded maximum degree have bounded dimension. Recently, Streib and Trotter proved …

The original notion of dimension for posets is due to Dushnik and Miller and has been
studied extensively in the literature. Quite recently, there has been considerable interest in …

We show that posets of bounded height whose cover graphs exclude a fixed graph as a
topological minor have bounded dimension. This result was already proven by Walczak …

Dimension is a key measure of complexity of partially ordered sets. Small dimension allows
succinct encoding. Indeed if P has dimension d, then to know whether x≤ y in P it is enough …

Dimension is a standard and well-studied measure of complexity of posets. Recent research
has provided many new upper bounds on the dimension for various structurally restricted …