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Art Gallery Theorem with Holes

  1. Apr 19, 2006 #1
    Hey guys, my professor recently posed the problem of finding a simple Fisk like proof for the Art Gallery Theorem with holes:

    it says thats to guard a polygon with n vertices and h holes, we will always need at most floor[(n+h)/3] where floor represents the floor function.

    now i saw some proofs, some used induction, others used the fact that we can split one of the hole vertices into 2 vertices and build channels, eliminating the hole and creating h vertices, so we would be left with a polygon with n+h vertices, and then we just apply the regular Art Gallery Theorem.

    however, I am trying to prove this theorem without using any perturbations.

    i'm just wondering if any of you guys have tried to solve this or have encountered a similar type problem in your studies, whatever studies it may be.
  2. jcsd
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