Drawing Graphs in the Hyperbolic Plane

  • Bojan Mohar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)

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.

References

  1. 1.
    E. M. Andreev, On convex polyhedra in Lobačevski\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{i} \) spaces, Mat. Sb. (N. S.) 81 (1970) 445–478; Engl. transl. in Math. USSR Sb. 10 (1970) 413-440.MathSciNetGoogle Scholar
  2. 2.
    E. M. Andreev, On convex polyhedra of finite volume in Lobačevski\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{i} \) space, Mat. Sb. (N. S.) 83 (1970) 256–260; Engl. transl. in Math. USSR Sb. 12 (1970) 255-259.MathSciNetGoogle Scholar
  3. 3.
    G. R. Brightwell, E. R. Scheinerman, Representations of planar graphs, SIAM J. Disc. Math. 6 (1993) 214–229.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Y. Colin de Verdière, Empilements de cercles: Convergence d’une méthode de point fixe, Forum Math. 1 (1989) 395–402.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Y. Colin de Verdière, Un principe variationnel pour les empilements des cercles, Invent. Math. 104 (1991) 655–669.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    B. Iversen, Hyperbolic geometry, Cambridge Univ. Press, 1992.MATHGoogle Scholar
  7. 7.
    P. Koebe, Kontaktprobleme auf der konformen Abbildung, Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 88 (1936) 141–164.Google Scholar
  8. 8.
    B. Mohar, Circle packings of maps in polynomial time, Europ. J. Combin. 18 (1997) 785–805. 136 B. MoharMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    B. Mohar, Circle packings of maps-The Euclidean case, Rend. Sem. Mat. Fis. (Milano), in press.Google Scholar
  10. 10.
    B. Mohar, C. Thomassen, Graphs on Surfaces, Johns Hopkins Univ. Press, to appear.Google Scholar
  11. 11.
    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.CrossRefGoogle Scholar
  12. 12.
    A. Ramsay, R. D. Richtmeyer, Introduction to Hyperbolic Geometry, Springer-Verlag, New York, 1995.MATHGoogle Scholar
  13. 13.
    J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.MATHGoogle Scholar
  14. 14.
    D. M. Y. Sommerville, The Elements of Non-Euclidean Geometry, Dover, New York, 1958.Google Scholar
  15. 15.
    S. Stahl, The Poincaré Half-Plane, Jones and Barlett Publishers, Boston, London, 1993.MATHGoogle Scholar
  16. 16.
    W. P. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. Lect. Notes, Princeton, NJ.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Bojan Mohar
    • 1
  1. 1.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia

Personalised recommendations