On grid intersection graphs

I. Ben Arroyo Hartman; Ilan Newman; Ran Ziv

doi:10.1016/0012-365X(91)90069-E

On grid intersection graphs

I. Ben Arroyo Hartman, Ilan Newman, Ran Ziv

Research output: Contribution to journal › Article › peer-review

Abstract

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 (x_i, y_j) ∈ E if and only if segments x_i and y_j intersect. We prove that all planar bipartite graphs have a grid representation, and exhibit some infinite families of graphs with no grid representation-among them the point line incidence graph of projective planes.

Original language	English
Pages (from-to)	41-52
Number of pages	12
Journal	Discrete Mathematics
Volume	87
Issue number	1
DOIs	https://doi.org/10.1016/0012-365X(91)90069-E
State	Published - 19 Jan 1991
Externally published	Yes

Bibliographical note

Funding Information:
* The research was done while the author was in the Mathematics Department, Technion, Israel, and the Computer Science Department, University of Toronto, Toronto, Canada. ** Supported by Technion V.P.R. Fund and New York Metropolitan research fund. *** The research was done while the author was in the Computer Science Department, Haifa, Israel.

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(91)90069-E

Cite this

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N2 - 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, yj) ∈ E if and only if segments xi and yj intersect. We prove that all planar bipartite graphs have a grid representation, and exhibit some infinite families of graphs with no grid representation-among them the point line incidence graph of projective planes.

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On grid intersection graphs

Abstract

Bibliographical note

ASJC Scopus subject areas

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