A Simple Linear Time Algorithm for Finding Even Triangulations of 2-Connected Bipartite Plane Graphs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Polychromatic colorings of plane graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
On Some City Guarding Problems
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Polychromatic 4-coloring of guillotine subdivisions
Information Processing Letters
On even triangulations of 2-connected embedded graphs
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Approximation algorithms for art gallery problems in polygons and terrains
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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The following graph-coloring result is proved: let $G$ be a 2-connected, bipartite, and plane graph. Then one can triangulate $G$ in such a way that the resulting graph is 3-colorable. Such a triangulation can be computed in $O(n^2)$ time. This result implies several new upper bounds for polygon guarding problems, including the first nontrivial upper bound for the rectilinear prison yard problem. (1) $\lfloor{n}/{3}\rfloor$ vertex guards are sufficient to watch the interior of a rectilinear polygon with holes. (2) $\lfloor{5n}/{12}\rfloor +3$ vertex guards ($\lfloor{n+4}/{3}\rfloor $ point guards) are sufficient to simultaneously watch both the interior and exterior of a rectilinear polygon. Moreover, a new lower bound of $\lfloor{5n}/{16}\rfloor$ vertex guards for the rectilinear prison yard problem is shown and proved to be asymptotically tight for the class of orthoconvex polygons.