The drawing of configurations

  • Harald Gropp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)


The drawing of configurations and other linear hypergraphs is discussed. From their historical and geometrical context it is quite natural to denote hyperedges of vertices as lines, i.e. to position the points (vertices) in the plane such that those points which form hyperedges are collinear in the plane (or as close to collinear as possible). This is a new concept in the area of hypergraph drawing. However, in mathematics it has been used for more than 100 years. The exact drawing of configurations is mainly based on the realization of matroids and techniques in computer algebra.


  1. 1.
    C. Berge, Hypergraphs, Amsterdam-New York-Oxford-Tokyo (1989)Google Scholar
  2. 2.
    J. Bokowski, B. Sturmfels, Computational Synthetic Geometry, Springer LNM 1355, Berlin-Heidelberg-New York (1989)Google Scholar
  3. 3.
    G. DiBattista, P. Eades, H. de Fraysseix, P. Rosenstiehl, R. Tamassia (eds.), Graph Drawing '93 Proceedings, September 1993, ParisGoogle Scholar
  4. 4.
    H. Gropp, On the history of configurations, Internat. Symp. on Structures in Math. Theories, ed. A.Díez, J.Echeverría, A.Ibarra, Universidad dei País Vasco, Bilbao (1990) 263–268Google Scholar
  5. 5.
    H. Gropp, Configurations and graphs, Discrete Math. 111 (1993) 269–276CrossRefGoogle Scholar
  6. 6.
    H. Gropp, Configurations and (r, 1)-designs, Discrete Math. 129 (1994) 113–137CrossRefGoogle Scholar
  7. 7.
    H. Gropp, Graph-like combinatorial structures in (r, 1)-designs, Discrete Math. 134 (1994) 65–73CrossRefGoogle Scholar
  8. 8.
    H. Gropp, Configurations and their realization (to appear)Google Scholar
  9. 9.
    H. Gropp, The (r, 1)-designs with 13 points (submitted to Discrete Math.)Google Scholar
  10. 10.
    S. Kantor, Die Configurationen (3,3)10, Sitzungsber. Akad. Wiss. Wien, math.-naturwiss. Kl. 84 (1881) 1291–1314Google Scholar
  11. 11.
    J.G. Oxley, Matroid theory, Oxford-New York-Tokyo (1992)Google Scholar
  12. 12.
    C. Pietsch, On the classification of linear spaces of order 11, J. Combin. Des. 3 (1995), 185–193Google Scholar
  13. 13.
    E. Steinitz, Über die Construction der Configurationen n3, Dissertation Breslau (1894)Google Scholar
  14. 14.
    V.I. Voloshin, On the upper chromatic number of a hypergraph, Australasian J. Comb. 11 (1995) 25–45Google Scholar
  15. 15.
    V.I. Voloshin, Hypergraph Drawing and Optimization System, preprintGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Harald Gropp
    • 1
  1. 1.HeidelbergGermany

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