On separability in discrete geometry

Abstract

A problem of Erd\H{o}s (Amer. Math. Monthly 52: 494-498, 1945) and a theorem of Fejes T\'oth and Fejes T\'oth (Acta Math. Acad. Sci. Hungar. 24: 229-232, 1973) initiated the study of non-separable arrangements of convex bodies and the investigation of totally separable packings of convex bodies with both topics analyzing the concept of separability from the point view of discrete geometry. This article surveys the progress made on these and some closely related problems and highlights the relevant questions that have been left open.