On convex partitions of polygonal regions Original Research Article

Let M ⊂ E2 be an open, connected and bounded polygonal region with polygonal holes of dimension d ∈ {0,1,2}. For a given set of boundary points x1, …, xn of M we derive the minimal number of convex pieces into which M can be divided such that for each xi, i = 1, …, n, the boundary of the final convex partition contains segments of suitably prescribed directions having xi as a common starting point. The proofs are based on graph theoretic arguments and elementary topology.