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.
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© 1999 Springer-Verlag Berlin Heidelberg
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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
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DOI: https://doi.org/10.1007/3-540-46784-X_27
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