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Gray Code Enumeration of Plane Straight-Line Graphs


We develop Gray code enumeration schemes for geometric straight-line graphs in the plane. The considered graph classes include plane graphs, connected plane graphs, and plane spanning trees. Previous results were restricted to the case where the underlying vertex set is in convex position.

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  • Aichholzer, O., Aurenhammer, F., Braß, P., Krasser, H.: Pseudo-triangulations from surfaces and a novel type of edge flip, SIAM J. Comput. 32, 1621–1653 (2003)

    Google Scholar 

  • Aichholzer, O., Aurenhammer, F., Krasser, H.: Enumerating order types for small point sets with applications, Order 19, 265–281 (2002)

    Google Scholar 

  • Aichholzer, O., Aurenhammer, F., Hurtado, F.: Sequences of spanning trees and a fixed tree theorem, Comput. Geom. Theory Appl. 21, 3–20 (2002)

    Google Scholar 

  • Ajtai, M., Chvátal, V., Newborn, M.M., Szemerédi, E.: Crossing-free subgraphs. Ann. Discrete Math. 12, 9–12 (1982)

    Google Scholar 

  • Arenas, R., Gonzalez, J., Marquez, A., Puertas Gonzalez, M.: Grafo de Grafos Planos de un Poligono Convexo. Jornadas de Matematica Discreta y Algoritmica 4, 31–38 (2004)

  • Avis, D., Fukuda, K.: Reverse search for enumeration, Discrete Appl. Math. 65, 21–46 (1996)

    Google Scholar 

  • Bereg, S.: Enumerating pseudo-triangulations in the plane, Comput. Geom. Theory Appl. 30, 207–222 (2005)

    Google Scholar 

  • Felsner, S.: On the number of arrangements of pseudolines, Discrete Comput. Geom. 18, 257–267 (1997)

    Google Scholar 

  • Hernando, M.C., Hurtado, F., Marquez, A., Mora, M., Noy, M.: Geometric tree graphs of points in convex position, Discrete Appl. Math. 93, 51–66 (1999)

    Google Scholar 

  • Hernando, M.C., Hurtado, F., Noy, M.: Graph of non-crossing perfect matchings. Graphs Combinat. 18, 517–532 (2002)

    Google Scholar 

  • Huemer, C., Hurtado, F., Noy, M., Omana-Pulido, E.: Gray codes for non-crossing partitions and dissections of a convex polygon. In: Proc. X Encuentros de Geometria Computacional, Sevilla, 2003, pp 20–23

  • Huemer, C., Hurtado, F., Pfeifle, J.: Gray codes and polytopal complexes for dissections of a polygon into k-gons. In: Proc. XI Encuentros de Geometria Computacional, Santander, 2005, pp 31–38

  • Hurtado, F., Noy, M.: Graph of triangulations of a convex polygon and tree of triangulations. Comput. Geom. Theory Appl. 13, 179–188 (1999)

    Google Scholar 

  • Hurtado, F., Noy, M., Urrutia, J.: Flipping edges in triangulations. Discrete Comput. Geom. 22, 333–346 (1999)

    Google Scholar 

  • Rivera-Campo, E., Urrutia-Galicia, V.: Hamilton cycles in the path graph of a set of points in convex position. Comput. Geom. Theory Appl. 18, 65–72 (2001)

    Google Scholar 

  • Ruskey, F.: Simple combinatorial Gray codes constructed by reversing sublists. Springer Lecture Notes in Computer Science, vol. 762 (1993), pp 201–208

  • Savage, C.: A survey of combinatorial Gray codes. SIAM Rev. 39, 605–629 (1997)

    Google Scholar 

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Correspondence to F. Aurenhammer.

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Research supported by the FWF Joint Research Project Industrial Geometry S9205-N12 and Projects MCYT-FEDER BFM2003-00368 and Gen. Cat 2005SGR00692.

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Aichholzer, O., Aurenhammer, F., Huemer, C. et al. Gray Code Enumeration of Plane Straight-Line Graphs. Graphs and Combinatorics 23, 467–479 (2007).

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  • Geometric graphs
  • enumeration scheme
  • Gray codes