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COMBINATORICS
2006

Orthogonal Art Galleries with Holes: A Coloring Proof of Aggarwal's Theorem

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Orthogonal Art Galleries with Holes: A Coloring Proof of Aggarwal's Theorem
We prove that n+h 4 vertex guards are always sufficient to see the entire interior of an n-vertex orthogonal polygon P with an arbitrary number h of holes provided that there exists a quadrilateralization whose dual graph is a cactus. Our proof is based upon 4-coloring of a quadrilateralization graph, and it is similar to that of Kahn and others for orthogonal polygons without holes. Consequently, we provide an alternate proof of Aggarwal's theorem asserting that n+h 4 vertex guards always suffice to cover any n-vertex orthogonal polygon with h 2 holes.
Pawel Zylinski
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Pawel Zylinski
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