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- W2069841121 abstract "In this paper we introduce a new method based on perfect graphs that can be used to prove bounds on the number of guards necessary to guard a rectilinear art gallery in terms of the number of vertices, area and perimeter, respectively. Using this method, we prove that a polyomino with perimeter (lge 6) can be guarded by at most (lfloor tfrac{l}{6}rfloor ) guards. Moreover, we give a new proof for the rectilinear art gallery theorem, stating that any rectilinear art gallery with (n) vertices can be guarded by at most (lfloor frac{n}{4}rfloor ) guards. Finally, we give a new proof that at most (lfloor tfrac{m+1}{3}rfloor ) guards are necessary to guard an (m)-polyomino, even if the polyomino contains holes." @default.
- W2069841121 created "2016-06-24" @default.
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- W2069841121 date "2014-04-01" @default.
- W2069841121 modified "2023-09-23" @default.
- W2069841121 title "Perfect Graphs and Guarding Rectilinear Art Galleries" @default.
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- W2069841121 doi "https://doi.org/10.1007/s00454-014-9587-4" @default.
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