Computing Radial Drawings on the Minimum Number of Circles

  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Henk Meijer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)


A radial drawing is a representation of a graph in which the vertices lie on concentric circles of finite radius. In this paper we study the problem of computing radial drawings of planar graphs by using the minimum number of concentric circles. We assume that the edges are drawn as straight-line segments and that co-circular vertices can be adjacent. It is proven that the problem can be solved in polynomial time.


  1. 1.
    Bachmaier, C., Brandenburg, F., Forster, M.: Radial level planarity testing and embedding in linear time. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 393–405. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Bachmaier, C., Brandenburg, F., Forster, M.: Track planarity testing and embedding. In: Proc. SOFSEM 2004, vol. 2, pp. 3–17 (2004)Google Scholar
  3. 3.
    Bienstock, D., Monma, C.L.: On the complexity of embedding planar graphs to minimize certain distance measures. Algorithmica 5(1), 93–109 (1990)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bornholdt, S., Schuster, H. (eds.): Handbook of Graphs and Networks: From the Genome to the Internet. Wiley-VCH, Chichester (2003)MATHGoogle Scholar
  5. 5.
    Cornelsen, S., Schank, T., Wagner, D.: Drawing graphs on two and three lines. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 31–41. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Di Giacomo, E., Didimo, W.: Straight-line drawings of 2-outerplanar graphs on two curves. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 419–424. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Di Giacomo, E., Didimo, W., Liotta, G., Wismath, S.K.: Curve-constrained drawings of planar graphs. Comp. Geometry: Theory and Appl. (to appear)Google Scholar
  8. 8.
    Dodge, M., Kitchin, R.: Atlas of Cyberspace. Addison-Wesley, Reading (2001)Google Scholar
  9. 9.
    Dorogstev, S.N., Mendes, J.F.F.: Evolution of Networks, From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003)Google Scholar
  10. 10.
    Harary, F.: Graph Theory. Addison-Wesley, Reading (1972)Google Scholar
  11. 11.
    Harary, F., Prins, G.: The block-cutpoint-tree of a graph. Publ. Math Debrecen 13, 103–107 (1966)MATHMathSciNetGoogle Scholar
  12. 12.
    Jünger, M., Mutzel, P. (eds.): Graph Drawing Software. Springer, Heidelberg (2003)MATHGoogle Scholar
  13. 13.
    Sugiyama, K.: Graph Drawing and Applications for Software and Knowldege Engineers. World Scientific, Singapore (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Henk Meijer
    • 2
  1. 1.Università degli Studi di PerugiaPerugiaItaly
  2. 2.School of ComputingQueen’s UniversityKingstonCanada

Personalised recommendations