Drawing Graphs in the Hyperbolic Plane

Mohar, Bojan (1999) Drawing Graphs in the Hyperbolic Plane. In: Graph Drawing 7th International Symposium, GD’99, September 15-19, 1999, Štirín Castle, Czech Republic , pp. 127-136 (Official URL: http://dx.doi.org/10.1007/3-540-46648-7_13).

Full text not available from this repository.

Abstract

It is shown how one can draw graphs on surfaces of negative Euler characteristic by using hyperbolic geometry and hyperbolic circle packing representations. The same approach applies to drawings of hyperbolic tessellations.

Item Type:Conference Paper
Additional Information:10.1007/3-540-46648-7_13
Classifications:M Methods > M.999 Others
G Algorithms and Complexity > G.490 Embeddings
P Styles > P.999 Others
ID Code:302

Repository Staff Only: item control page

References

E. M. Andreev, On convex polyhedra in Lobacevskii spaces, Mat. Sb. (N. S.) 81 (1970) 445-478; Engl. transl. in Math. USSR Sb. 10 (1970) 413-440.

E. M. Andreev, On convex polyhedra of finite volume in Lobacevskii space, Mat. Sb. (N. S.) 83 (1970) 256-260; Engl. transl. in Math. USSR Sb. 12 (1970) 255-259.

G. R. Brightwell, E. R. Scheinerman, Representations of planar graphs, SIAM J. Disc. Math. 6 (1993) 214-229.

Y. Colin de Verdière, Empilements de cercles: Convergence d'une méthode de point fixe, Forum Math. 1 (1989) 395-402.

Y. Colin de Verdière, Un principe variationnel pour les empilements des cercles, Invent. Math. 104 (1991) 655-669.

B. Iversen, Hyperbolic geometry, Cambridge Univ. Press, 1992.

P. Koebe, Kontaktprobleme auf der konformen Abbildung, Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 88 (1936) 141-164.

B. Mohar, Circle packings of maps in polynomial time, Europ. J. Combin. 18 (1997) 785-805.

B. Mohar, Circle packings of maps - The Euclidean case, Rend. Sem. Mat. Fis. (Milano), in press.

B. Mohar, C. Thomassen, Graphs on Surfaces, Johns Hopkins Univ. Press, to appear.

T. Munzner, Drawing large graphs with H3Viewer and Site Manager (system demonstration), in "Graph Drawing '98", Lecture Notes in Computer Science, Springer-Verlag, 1998, pp. 384-393.

A. Ramsay, R. D. Richtmeyer, Introduction to Hyperbolic Geometry, Springer-Verlag, New York, 1995.

J. G. Ratcliffe, Foundations of Hyberbolic Manifolds, Springer-Verlag, New York, 1994.

D. M. Y. Sommerville, The Elements of Non-Euclidean Geometry, Dover, New York, 1958.

S. Stahl, The Poincaré Half-Plane, Jones and Barlett Publishers, Boston, London, 1993.

W. P. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. Lect. Notes, Princeton, NJ.