67 citations · 180 across the 16 of their papers we have counts for
6 papers · 1 filter
Local Dimension is Unbounded for Planar Posets
Bartłomiej Bosek, Jarosław Grytczuk, William T. Trotter
In 1981, Kelly showed that planar posets can have arbitrarily large dimension. However, the posets in Kelly's example have bounded Boolean dimension and bounded local dimension, le…
Comparing Dushnik-Miller Dimension, Boolean Dimension and Local Dimension
Fidel Barrera-Cruz, Thomas Prag, Heather Smith +2
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…
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…
Burling graphs, chromatic number, and orthogonal tree-decompositions
Stefan Felsner, Gwenaël Joret, Piotr Micek +2
A classic result of Asplund and Grünbaum states that intersection graphs of axis-aligned rectangles in the plane are -bounded. This theorem can be equivalently stated in terms o…
Separating Tree-chromatic number from Path-chromatic Number
Fidel Barrera-Cruz, Stefan Felsner, Tamás Mészáros +4
We apply Ramsey theoretic tools to show that there is a family of graphs which have tree-chromatic number at most~ while the path-chromatic number is unbounded. This resolves a…