Abstract

This paper examines an infinite family of proximity drawings of graphs called open and closed fi-drawings, first defined by Kirkpatrick and Radke [15, 21] in the context of computational morphology. Such proximity drawings include as special cases the well-known Gabriel, relative neighborhood and strip drawings. Complete characterizations of those trees that admit open fi-drawings for 0 fi ! fi ! 1 or closed fi-drawings for 0 fi ! fi 1 are given, as well as partial characterizations for other values of fi. For the intervals of fi in which complete characterizations are given, it can be determined in linear time whether a tree admits an open or closed fi-drawing, and, if so, such a drawing can be computed in linear time in the real RAM model. Finally, a complete characterization of all graphs which admit closed strip drawings is given.

Citations