A Counterexample for the Sufficiency of Edge Guards in Star Polygons

Abstract It has been established by Toussaint that ⌊ n ⧸5⌋ edge guards are necessary for guarding a star polygon of n -vertices. Whether this many edge guards are always sufficient has remained an open problem. We show in this paper that ⌊ n ⧸5⌋ guards are not sufficient to guard a star polygon of n -vertices.