Art galleries with interior walls (Q1302041)

Let an art gallery be formed by walls constituting an \(n\)-sided polygon, \(m\) vertices of which are joined by non-intersecting interior diagonals, called interior walls, each having small arbitrarily placed doorways. The author proves that the minimum number of guards necessary to guard an art gallery with n corners and m interior walls is \( \min\{[(2n-3)/3 ],[(2n+m-2)/4] ,[(2m+n)/3 ]\}\). If a gallery with convex rooms are taken into consideration of size at least \(r\), the former result improves to \( \min\{m,[(m+n)/r ] \}\).