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.
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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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