A nine-vertex polygon is the smallest art gallery whose every-third-vertex guarding scheme fails for every choice of starting vertex.
O’Rourke, Art gallery theorems and algorithms, International Series of Monographs on Computer Science, The Clarendon Press, Oxford Uni- versity Press, New York, 1987
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The smallest art gallery not guarded by every third vertex
A nine-vertex polygon is the smallest art gallery whose every-third-vertex guarding scheme fails for every choice of starting vertex.