partitioning

Art gallery theorems

Art gallery theorems are concerned with the number of guards required to control a polygon, and many variations exist depending on how much power the guards have and what kind of restrictions are imposed on the polygon. Even though by nature these …

Partitioning orthogonal polygons into at most 8-vertex pieces, with application to an art gallery theorem

We prove that every simply connected orthogonal polygon of $n$ vertices can be partitioned into $\lfloor\frac{3n+4}{16}\rfloor$ (simply connected) orthogonal polygons of at most 8 vertices. It yields a new and shorter proof of the theorem of A. …