Abstract
The twisted graph T n is a complete topological graph with n vertices v1,v2,…,v n in which two edges v i v j (i < j) and v s v t (s < t) cross each other if and only if i < s < t < j or s < i < j < t. We study several properties concerning plane topological subgraphs of T n .
Partially supported by Conacyt, México, project 83856.
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References
Akiyama, J., Urrutia, J.: Simple alternating path problem. Discrete Math. 84(1), 101–103 (1990)
Avis, D., Fukuda, K.: Reverse search enumeration. Discrete Applied Math. 6, 21–46 (1996)
Hajnal, P., Mészáros, V.: Note on noncrossing alternating path in colored convex sets. Accepted in Discrete Mathematics and Theoretical Computer Science
Harborth, H., Mengersen, I.: Drawings of the complete graph with maximum number of crossings. In: Proceedings of the Graph Theory and Computing, Boca Raton, Fl. Congressus Numerantium, vol. 88, pp. 225–228. Utilitas Math., Winnipeg (1992)
Hernando, C., Hurtado, F., Noy, M.: Graphs of non-crossing perfect matchings. Graphs and Combin. 18, 517–532 (2002)
Klazar, M.: Counting pattern-free set partitions II. Noncrossing and other hypergraphs. Electron. J. Combin. 7, Research Paper 34, 25 pages (2000)
Kynčl, J., Pach, J., Tóth, G.: Long alternating paths in bicolored point sets. Discrete Math. 308(19), 4315–4321 (2008)
Lawson, C.L.: Software for C1-interpolation. In: Rice, J. (ed.) Mathematical Software III, pp. 161–194. Academic Press, New York (1977)
Pach, J., Solymosi, J., Tóth, G.: Unavoidable configurations in complete topological graphs. Discrete Comput. Geom. 30, 311–320 (2003)
Rivera-Campo, E.: A Note on the Existente of Plane Spanning Trees of Geometrie Graphs. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 1998. LNCS, vol. 1763, pp. 274–277. Springer, Heidelberg (2000)
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Omaña-Pulido, E., Rivera-Campo, E. (2012). Notes on the Twisted Graph. In: Márquez, A., Ramos, P., Urrutia, J. (eds) Computational Geometry. EGC 2011. Lecture Notes in Computer Science, vol 7579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34191-5_11
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DOI: https://doi.org/10.1007/978-3-642-34191-5_11
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