Ferrers dimension of grid intersection graphs
نویسندگان
چکیده
منابع مشابه
Grid Intersection Graphs and Order Dimension
We study bipartite geometric intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is a grid intersection graph have order dimension at most four. Starting from this observation we look at various classes of graphs between grid intersection graph and bipartite permutations graphs and the containment relation on these cla...
متن کاملOn grid intersection graphs
Hartman I.B.-A., I. Newman and R. Ziv, On grid intersection graphs, Discrete Mathematics 87 (1991) 41-52. A bipartite graph G = (X, Y; E) has a grid representation if X and Y correspond to sets of horizontal and vertical segments in the plane, respectively, such that (xi, y,) E E if and only if segments x, and y, intersect. We prove that all planar bipartite graphs have a grid representation, a...
متن کاملIntersection Dimension of Bipartite Graphs
We introduce a concept of intersection dimension of a graph with respect to a graph class. This generalizes Ferrers dimension, boxicity, and poset dimension, and leads to interesting new problems. We focus in particular on bipartite graph classes defined as intersection graphs of two kinds of geometric objects. We relate well-known graph classes such as interval bigraphs, two-directional orthog...
متن کاملFerrers dimension and boxicity
This note explores the relation between the boxicity of undirected graphs and the Ferrers dimension of digraphs.
متن کاملGrid intersection graphs and boxicity
A graph has hyuiciry k if k is the smallest integer such that G is an intersection graph of k-dimensional boxes in a &-dimensional space (where the sides of the boxes are parallel to the coordinate axis). A graph has grid dimension k if k is the smallest integer such that G is an intersection graph of k-dimensional boxes (parallel to the coordinate axis) in a (k+ I)-dimensional space. We prove ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.05.035