Intersection of maximal orthogonally starshaped polygons

Let S be a simply connected orthogonal polygon in and let P(S) denote the intersection of all maximal starshaped via staircase paths orthogonal subpolygons in S. Our result: if , then there exists a maximal starshaped via staircase paths orthogonal polygon , such that . As a corollary, P(S) is a starshaped (via staircase paths) orthogonal polygon or empty. The results fail without the requirement that the set S is simply connected. Received 1 March 1999.