Abstract
Lai and Leinwand have shown that an arbitrary plane (i.e., embedded planar) graph G can be transformed, bya dding crossover vertices, into a new plane graph G′ admitting a rectangular dual. Moreover, theyc onjectured that finding a minimum set of such crossover vertices is an NP-complete problem. In this paper it is shown that the above problem can be resolved in polynomial time by reducing it to a graph covering problem, and an efficient algorithm for finding a minimum set of edges on which to insert the crossover vertices is also presented.
A graph theoretic description of the circuit.
Four of them never meeting in a single point.
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
M. Ancona, L. De Floriani, J. S. Deogun, Path Problems in Structured Graphs,The Computer Journal, V. 29, N. 6, 1986, pp. 553–563. 282
K. Kozminski, E. Kinnen, Rectangular dual of planar graphs, Networks 5 (1985), pp. 145–157. 278, 280
J. Bhasker, S. Sahni, A linear algorithm to check for the existence of a rectangular dual of a planar triangulated graph, Networks 7 (1987), pp. 307–317. 278
T. Biedl, G. Kant, M. Kaufmann, On Triangulating Planar Graphs under the Four-Connectivity Constraint, Proc. of SWAT94, LNCS Vol. 824, Springer Verlag, 1994, pp. 83–94. 278
M. Gondran, M. Minoux, Graphs and Algorithms, John Wiley-Interscience Pubblication, 1984
Y. Lai, M. Leinwand, Algorithms for Floorplan Design Via Rectangular Dualization, IEEE Transactions on Computer-Aided Design, V. 7, N. 12, De. 1988, pp. 1278–1289. 278, 279, 280
G. Kant, X. He, Two Algorithms for Finding Rectangular Duals of Planar Graphs, Procs. WG’93, LNCS Vol. 790, Springer Verlag 1994, pp. 396–410.
Z. Galil, Efficient Algorithms for Maximum Matching in Graphs, ACM Computing Surveys, Vol. 18, N. 1, pp. 23–38, March 1986. 287, 289
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Accornero, A., Ancona, M., Varini, S. (1999). All Separating Triangles in a Plane Graph Can Be Optimally “Broken” in Poly nomial Time. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_27
Download citation
DOI: https://doi.org/10.1007/3-540-46784-X_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66731-5
Online ISBN: 978-3-540-46784-7
eBook Packages: Springer Book Archive