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 …

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 …

We prove that every planar poset P of height h has dimension at most 192h+96. This
improves on previous exponential bounds and is best possible up to a constant factor. We …

A ladder is a 2× k grid graph. When does a graph class\cal CC exclude some ladder as a
minor? We show that this is the case if and only if all graphs G in\cal CC admit a proper …

We show that height $ h $ posets that have planar cover graphs have dimension $\mathcal
{O}(h^ 6) $. Previously, the best upper bound was $2^{\mathcal {O}(h^ 3)} $. Planarity plays …

It has been known for more than 40 years that there are posets with planar cover graphs and
arbitrarily large dimension. Recently, Streib and Trotter proved that such posets must have …

The goal of this dissertation is to study the various connections between the dimension of
posets and graph theoretic properties of their cover graphs. We are particularly interested in …

In recent years, researchers have shown renewed interest in combinatorial properties of
posets determined by geometric properties of its order diagram and topological properties of …