Abstract
We prove the following graph coloring result: Let G be a 2-connected bipartite planar graph. Then one can triangulate G in such a way that the resulting graph is 3-colorable.
This result implies several new upper bounds for guarding problems including the first non—trivial upper bound for the rectilinear Prison Yard Problem:
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1.
[n/3] vertex guards are sufficient to watch the interior of a rectilinear polygon with holes.
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2.
[5n/12] + 3 vertex guards resp. [n+4/3] point guards are sufficient to watch simultaneously both the interior and exterior of a rectilinear polygon.
Moreover, we show a new lower bound of [5n/16] vertex guards for the rectilinear Prison Yard Problem and prove it to be asymptotically tight for the class of orthoconvex polygons.
Both authors have been partially supported by the ESPRIT Basic Research Action project ALCOM II and the Wissenschaftler-Integrationsprogramm Berlin.
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© 1993 Springer-Verlag Berlin Heidelberg
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Hoffmann, F., Kriegel, K. (1993). A graph coloring result and its consequences for some guarding problems. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_237
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DOI: https://doi.org/10.1007/3-540-57568-5_237
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