23 citations · 23 across the 1 of their papers we have counts for
6 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…
Fractional Local Dimension
Heather C. Smith, William T. Trotter
The original notion of dimension for posets was introduced by Dushnik and Miller in 1941 and has been studied extensively in the literature. In 1992, Brightwell and Scheinerman dev…
The Graph of Critical Pairs of a Crown
Fidel Barrera-Cruz, Rebecca Garcia, Pamela Harris +5
There is a natural way to associate with a poset a hypergraph , called the hypergraph of critical pairs, so that the dimension of is exactly equal to the chromatic numbe…
Boolean dimension and local dimension
William T. Trotter, Bartosz Walczak
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 cl…
First-fit coloring on interval graphs has performance ratio at least 5
H. A. Kierstead, David A. Smith, W. T. Trotter
First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighb…