Intersection of maximal orthogonally starshaped polygons

Abstract

Let S be a simply connected orthogonal polygon in $ R^2 $ and let P(S) denote the intersection of all maximal starshaped via staircase paths orthogonal subpolygons in S. Our result: if $ P(S)\ne \emptyset $ , then there exists a maximal starshaped via staircase paths orthogonal polygon $ T\subseteq S $ , such that $ KerT\subseteq KerP(S) $ . 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.