Abstract
In this paper we consider a variation of the Art Gallery Problem. A set of points \( \mathcal{G} \) in a polygon P n is a connected guard set for P n provided that is a guard set and the visibility graph of the set of guards \( \mathcal{G} \) in P n is connected. We use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is ⌊n − 2)/2⌋. This result was originally established by induction by Hernández-Peñalver [3]. From this result it easily follows that if the art gallery is orthogonal (each interior angle is 90° or 270°), then the minimum number of connected guards is n/2 − 2.
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References
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© 2003 Springer-Verlag Berlin Heidelberg
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Pinciu, V. (2003). A Coloring Algorithm for Finding Connected Guards in Art Galleries. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. DMTCS 2003. Lecture Notes in Computer Science, vol 2731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45066-1_20
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DOI: https://doi.org/10.1007/3-540-45066-1_20
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