Art Gallery Theorems

Authors

  • Luigi Togliani Liceo Scientifico “Belfiore”, Mantova (Italy)

DOI:

https://doi.org/10.23756/sp.v6i2.440

Keywords:

art gallery, polygon triangulations, orthogonal polygon

Abstract

Some important results about art gallery theorems are proposed, starting from Chvátal’s essay, using also polygon triangulations and orthogonal polygons.

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References

Aggarwal A. (1984). The Art Gallery Theorem: Its Variations, Applications, and Algorithmic Aspects. Ph.D. Thesis, The Johns Hopkins University.

Bajuelos, A.L.; Canales, S.; Hernández, G. and Martins, M. A. (2007). “Solving some Combinatorial Problems in grid n-ogons”. International Journal on Mathematics and Computers in Simulation, 2, 1, 177-183.

Chvátal, V. (1975). “A combinatorial theorem in plane geometry”. Journal of Combinatorial Theory (B) 18, 39-41.

Elnagar, A. and Lulu, L. (2004). “Guarding polygons with holes for robot motion planning applications”. 2004 IEEE International Conference on Systems, Man and Cybernetics, 1, 923-928.

Fisk, S. (1978). “A Short Proof of Chvátal’s Watchman Theorem”. Journal of Combinatorial Theory (B) 24, 374.

Hoffmann F.; Kriegel K. (1996). “A graph coloring result and its consequences for polygon guarding problems”. SIAM J. Discrete Mathematics, 9(2), 210-224.

Kaul, H. (2014). The Art Gallery Problem. Chicago: Illinois Institute of Technology.

http://www.math.iit.edu/~kaul/talks/LongArtGalleryTalk.pdf (ultimo accesso: 19-07-2018).

Kahn, J.; Klawe, M.M. and Kleitman, D. (1980). “Traditional Galleries Require Fewer Watchmen”. SIAM Journal on Algebraic and Discrete Methods. 4. 10.1137/0604020.

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Published

2018-12-31

Issue

Vol. 6 No. 2 (2018)

Section

Volume 6 Issue 2 2018

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