The order dimension of the complete graph

@article{Hosten1999TheOD,
  title={The order dimension of the complete graph},
  author={Serkan Hosten and Walter D. Morris},
  journal={Discret. Math.},
  year={1999},
  volume={201},
  pages={133-139}
}
View via Publisher
doi.org
42 Citations
Highly Influential Citations
6
Background Citations
17
Methods Citations
4
Results Citations
4

42 Citations

Citation Type

Citation Type

The dimension of two levels of the Boolean lattice
Coloring copoints of a planar point set
Incidence Posets and Cover Graphs
TLDR
It is shown that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two and two, respectively.
The maximum number of edges in a graph of bounded dimension, with applications to ring theory
Posets and planar graphs
TLDR
A refined version of dimension for graphs which can assume a value between t − 1 and t is introduced, which is equivalent to the classical combinatorial problem known as Dedekind’s problem.
Homomorphism and Dimension
The dimension of a graph, that is, the dimension of its incidence poset, has become a major bridge between posets and graphs. Although allowing a nice characterization of planarity, this dimension…
Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets
Chromatic numbers of copoint graphs of convex geometries
From planar graphs to higher dimension
In this thesis we look for generalizations of some properties of planar graphs to higher dimensions by replacing graphs by simplicial complexes. In particular we study the Dushnik-Miller dimension…
Empty Rectangles and Graph Dimension
We consider rectangle graphs whose edges are defined by pairs of points in diagonally opposite corners of empty axis-aligned rectangles. The maximum number of edges of such a graph on n points is…
...
...

References

SHOWING 1-10 OF 11 REFERENCES
Planar graphs and poset dimension
We view the incidence relation of a graph G=(V. E) as an order relation on its vertices and edges, i.e. a<Gb if and only of a is a vertex and b is an edge incident on a. This leads to the definition…
On Dedekind’s problem: the number of isotone Boolean functions. II
It is shown that 0(n), the size of the free distributive lattice on n generators (which is the number of isotone Boolean functions on subsets of an n element set), satisfies [n1 i (n) < 2(1 +0(1og…
A computation of the eighth Dedekind number
We compute the eighth Dedekind number, or the number of monotone collections of subsets of a set with eight elements. The number obtained is 56, 130, 437, 228, 687, 557, 907, 788.
Minimal scrambling sets of simple orders
Abstract : Let 2 < or = k < n be fixed integers, a family F of simple orders on an n element set is said to be k-suitable if of every k elements in the n set, each one is the largest of the k in some…
The number of outside corners of monomial ideals
Combinatorics and Partially Ordered Sets: Dimension Theory
Primarily intended for research mathematicians and computer scientists, Combinatorics and Partially Ordered Sets: Dimension Theory also serves as a useful text for advanced students in either field.…
Concerning a certain set of arrangements
there exists an arrangement in S in which ak follows all the a, with i < k. Such sets S surely exist; for example, any set of m arrangements whose terminal elements are 1, 2, , m, respectively, will…
Monomial Resolutions
Call a monomial ideal M "generic" if no variable appears with the same nonzero exponent in two distinct monomial generators. Using a convex polytope first studied by Scarf, we obtain a minimal free…
Theory of convex structures
Algebra: 117-118
...
...