Grid Intersection and Box Intersection Graphs on Surfaces

Kratochvíl, Jan and Przytycka, Teresa (1996) Grid Intersection and Box Intersection Graphs on Surfaces. In: Symposium on Graph Drawing, GD 1995, September 20-22, 1995, Passau, Germany , pp. 365-372 (Official URL:

Full text not available from this repository.


As analogs to grid intersection graphs and rectangle intersection graphs in the plane, we consider grid intersection graphs, grid contact graphs and box intersection graphs on the other two euclidean surfaces - the annulus and the torus. Our first results concern the inclusions among these classes, and the main result is negative - there are bipartite box intersection graphs on annulus (torus), which are not grid intersection graphs on the particular surfaces (in contrast to the planar case, where the two classes are equal, cf. Bellantoni, Hartman, Przytycka, Whitesides: Grid intersection graphs and boxicity, Discrete Math. 114 (1993), 41-49). We also consider the question of computational complexity of recognizing these classes. Among other results, we show that recognition of grid intersection graphs on annulus and torus are both polynomial time solvable, provided orderings of both vertical and horizontal segments are specified.

Item Type:Conference Paper
Additional Information:10.1007/BFb0021820
Classifications:Z Theory > Z.250 Geometry
M Methods > M.100 Algebraic
G Algorithms and Complexity > G.560 Geometry
ID Code:179

Repository Staff Only: item control page


Bellantoni, S., Ben-Arroyo Hartman, I., Przytycka, T., Whitesides, S.: Grid intersection graphs and boxicity, Discrete Math. 114 (1993), 41-49

Cozzens, M. B., Roberts, F. S.: On dimensional properties of graphs, Graphs and Combinatorics 5 (1989), 29-46

de Fraysseix, H., de Mendez, P. O., Pach, J.: Representation of planar graphs by segments, Intuitive Geometry, Colloquia Mathematica Societatos Janos Bolyai 63 (1991), 109-117

Kratochvíl, J.: A special planar satisfiability problem and a consequence of its NP-completeness, Discrete Appl. Math. 52 (1994) 233-252

Mohar, B. (private communication)

Mohar, B., Rosenstiehl, P.: Tessellation and visibility representations of maps on the torus (preprint)

Roberts, F. S.: On the boxicity and cubicity of a graph, In: W. T. Tutte, ed., Recent Progress in Combinatorics, Academic Press, New York, 1969, pp. 301-310

Rosenstiehl, P., Tarjan, R. E.: Rectilinear planar layouts and bipolar orientations of graphs, Discrete Comput. Geometry 1 (1986), 343-353

Tamassia, R., Tollis, I. G.: A unified approach to visibility representations of planar graphs, Discrete Comput. Geometry 1 (1986), 321-341

Wood, D.: The riches of rectangles, In: Proceedings 5th International Meeting of Young Computer Scientists, Smolenice (1988), 67-75.