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.
Bibliographical noteFunding 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