25 citations · 46 across the 5 of their papers we have counts for
7 papers
Random bipartite posets and extremal problems
Csaba Biró, Peter Hamburger, H. A. Kierstead +3
Previously, Erdős, Kierstead and Trotter investigated the dimension of random height~ partially ordered sets. Their research was motivated primarily by two goals: (1)~analyzing…
Planar Posets that are Accessible from Below Have Dimension at Most 6
Csaba Biró, Bartłomiej Bosek, Heather C. Smith +3
Planar posets can have arbitrarily large dimension. However, a planar poset of height has dimension at most , while a planar poset with minimal elements has dimens…
Dimension of posets with planar cover graphs excluding two long incomparable chains
David M. Howard, Noah Streib, William T. Trotter +2
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 h…
Dimension and cut vertices: an application of Ramsey theory
William T. Trotter, Bartosz Walczak, Ruidong Wang
Motivated by quite recent research involving the relationship between the dimension of a poset and graph-theoretic properties of its cover graph, we show that for every ,…
On the dimension of posets with cover graphs of treewidth
Gwenaël Joret, Piotr Micek, William T. Trotter +2
In 1977, Trotter and Moore proved that a poset has dimension at most whenever its cover graph is a forest, or equivalently, has treewidth at most . On the other hand, a well…
Incidence Posets and Cover Graphs
William T. Trotter, Ruidong Wang
We prove two theorems concerning incidence posets of graphs, cover graphs of posets and a related graph parameter. First, answering a question of Haxell, we show that the chromatic…
Tree-width and dimension
Gwenaël Joret, Piotr Micek, Kevin G. Milans +3
Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural grap…