Abstract
Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of the various attempts to answer it.
As flips are a topic close to Ferran Hurtado’s heart, we would like to dedicate this article to him on the occasion of his 60th birthday.
Research supported in part by NSERC.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aichholzer, O., Huemer, C., Krasser, H.: Triangulations without pointed spanning trees. Comput. Geom. 40(1), 79–83 (2008)
Bose, P., Hurtado, F.: Flips in planar graphs. Comput. Geom. 42(1), 60–80 (2009)
Bose, P., Jansens, D., van Renssen, A., Saumell, M., Verdonschot, S.: Making triangulations 4-connected using flips. In: Proceedings of the 23rd Canadian Conference on Computational Geometry, pp. 241–247 (2011); A full version of this paper can be found at arXiv:1110.6473
Gao, Z., Urrutia, J., Wang, J.: Diagonal flips in labelled planar triangulations. Graphs Combin. 17(4), 647–657 (2001)
Komuro, H.: The diagonal flips of triangulations on the sphere. Yokohama Math. J. 44(2), 115–122 (1997)
Mori, R., Nakamoto, A., Ota, K.: Diagonal flips in Hamiltonian triangulations on the sphere. Graphs Combin. 19(3), 413–418 (2003)
Negami, S., Nakamoto, A.: Diagonal transformations of graphs on closed surfaces. Sci. Rep. Yokohama Nat. Univ. Sect. I Math. Phys. Chem. 40, 71–97 (1993)
Wagner, K.: Bemerkungen zum vierfarbenproblem. Jahresber. Dtsch. Math.-Ver. 46, 26–32 (1936)
Whitney, H.: A theorem on graphs. Ann. of Math. (2) 32(2), 378–390 (1931)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bose, P., Verdonschot, S. (2012). A History of Flips in Combinatorial Triangulations. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-34191-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34190-8
Online ISBN: 978-3-642-34191-5
eBook Packages: Computer ScienceComputer Science (R0)