Interval bigraphs are unit grid intersection graphs

Unit Grid Intersection Graphs: Recognition and Properties

It has been known since 1991 that the problem of recognizing grid intersection graphs is NP-complete. Here we use a modified argument of the above result to show that even if we restrict to the class of unit grid intersection graphs (UGIGs), the recognition remains hard, as well as for all graph classes contained inbetween. The result holds even when considering only graphs with arbitrarily lar...

On 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...

Grid 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 ...

Unit Mixed Interval Graphs

In this paper we extend the work of Rautenbach and Szwarcfiter [8] by giving a structural characterization of graphs that can be represented by the intersection of unit intervals that may or may not contain their endpoints. A characterization was proved independently by Joos in [6], however our approach provides an algorithm that produces such a representation, as well as a forbidden graph char...

Bipartite probe interval graphs, circular arc graphs, and interval point bigraphs