Boolean Dimension and Local Dimension
TLDR
In this article, the authors focus on boolean dimension and local dimension, and determine precisely which values of dimension/boolean dimension/local dimension imply that the two other parameters are bounded.About:
This article is published in Electronic Notes in Discrete Mathematics.The article was published on 2017-08-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Order dimension & Dimension (vector space).read more
Citations
More filters
Posted Content
Local Dimension is Unbounded for Planar Posets
TL;DR: In this paper, it was shown that the local dimension of a planar poset is not bounded in terms of the maximum local dimension, but rather the tree-width of its cover graph, independent of its height.
Journal ArticleDOI
Comparing Dushnik-Miller Dimension, Boolean Dimension and Local Dimension
TL;DR: It is proved that the local dimension of a poset cannot be bounded in terms of the tree-width of its cover graph, independent of height.
Posted Content
Comparing Dushnik-Miller Dimension, Boolean Dimension and Local Dimension
TL;DR: In this paper, it was shown that the local dimension of a poset cannot be bounded in terms of the tree-width of its cover graph, independent of its height, and that the poset's local dimension is bounded by the path width of the cover graph.
Posted Content
Boolean Dimension, Components and Blocks
TL;DR: In this paper, the authors investigated the behavior of Boolean dimension with respect to components and blocks, and they showed that Boolean dimension behaves like Dushnik-Miller dimension in terms of both component and block dimensions.
Book ChapterDOI
Local and Union Page Numbers
Laura Merker,Torsten Ueckerdt +1 more
TL;DR: In this paper, the authors introduce the concepts of local and union book embeddings, and, as the corresponding graph parameters, the local page number and the union page number are relaxations of the classical page number.
References
More filters
Journal ArticleDOI
Partial orders of dimension 2
Journal ArticleDOI
The dimension of planar posets
William T. Trotter,John I. Moore +1 more
TL;DR: It is shown that the dimension of a tree is at most three and the forbidden subposet characterization of two-dimensional trees is given and given to the graph-theoretic sense.
Journal ArticleDOI
On the dimension of partially ordered sets
TL;DR: The topic of the title is studied in some detail and the main results are summarized in the first four paragraphs of this paper.