How to Draw a Tait-Colorable Graph

  • David A. Richter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)


Presented here are necessary and sufficient conditions for a cubic graph equipped with a Tait-coloring to have a drawing in the real projective plane where every edge is represented by a line segment, all of the lines supporting the edges sharing a common color are concurrent, and all of the supporting lines are distinct.


Realization Space Simple Cycle Forced Pair Combinatorial Direction Real Projective Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Agol, I., Hass, J., Thurston, W.: The computational complexity of knot genus and spanning area. Trans. Amer. Math. Soc. 358(9), 3821–3850 (2006), (electronic), MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Biggs, N.: Algebraic graph theory. cambridge Tracts in Mathematics, vol. 67, Cambridge University Press, London (1974)Google Scholar
  3. 3.
    Björner, A., Vergnas, M.L., Sturmfels, B., White, N., Ziegler, G.M.: Oriented Matroids, 2nd edn. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  4. 4.
    Bonnington, C.P., Little, C.H.C.: The Foundations of Topological Graph Theory. Springer, New York (1995)CrossRefzbMATHGoogle Scholar
  5. 5.
    Eppstein, D.: The topology of bendless three-dimensional orthogonal graph drawing. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 78–89. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Eppstein, D., Mumford, E.: Steinitz theorems for orthogonal polyhedra (December 2009) arXiv:0912.0537Google Scholar
  7. 7.
    Ferri, M., Gagliardi, C., Grasselli, L.: A graph-theoretical representation of pl-manifolds—a survey on crystallizations. Aequationes Math. 31(2-3), 121–141 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ivanov, S.V.: The computational complexity of basic decision problems in 3-dimensional topology. Geom. Dedicata 131, 1–26 (2008), MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Keszegh, B., Pach, J., Pálvölgyi, D., Tóth, G.: Drawing cubic graphs with at most five slopes. Comput. Geom. 40(2), 138–147 (2008), MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Richter, D.A.: Ghost symmetry and an analogue of Steinitz’s theorem. Contrib. Alg. Geom. ( to appear, 2010)Google Scholar
  11. 11.
    Richter-Gebert, J.: Realization Spaces of Polytopes. Lecture Notes in Mathematics, vol. 1643. Springer, Heidelberg (1996)zbMATHGoogle Scholar
  12. 12.
    Richter-Gebert, J., Kortenkamp, U.H.: The interactive geometry software Cinderella. Springer-Verlag, Heidelberg (1999); with 1 CD-ROM (Windows, MacOS, UNIX and JAVA-1.1 platform)Google Scholar
  13. 13.
    Tutte, W.T.: Graph Theory, Encyclopedia of Mathematics and its Applications, vol. 21. Addison-Wesley Publishing Company, Menlo Park (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • David A. Richter
    • 1
  1. 1.Western Michigan UniversityKalamazooUSA

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