7 papers
Notes on uniform contractions of congruent balls
Károly Bezdek
In this note, we obtain stronger results on uniform contractions of intersections and unions of congruent balls, thereby extending previous partial confirmations of the Kneser-Poul…
On basic -ball polyhedra
Károly Bezdek
This note introduces the class of basic -ball polyhedra in the -dimensional Euclidean space for and . We investigate their face structure and, for…
Non-separable arrangements of convex bodies revisited
Károly Bezdek, Zsolt Lángi
A problem posed by Erdős in 1945 initiated the study of non-separable arrangements of convex bodies. A finite collection of convex bodies in Euclidean -space is called a non-sep…
Selected topics from the theory of intersections of balls
Károly Bezdek, Zsolt Lángi, Márton Naszódi
In this survey, we discuss volumetric and combinatorial results concerning (mostly finite) intersections or unions of balls (mostly of equal radii) in the -dimensional real vect…
On separability in discrete geometry
Károly Bezdek, Zsolt Lángi
A problem of Erdős (Amer. Math. Monthly 52: 494-498, 1945) and a theorem of Fejes Tóth and Fejes Tóth (Acta Math. Acad. Sci. Hungar. 24: 229-232, 1973) initiated the study of non-s…
Density bounds for unit ball packings relative to their outer parallel domains
Károly Bezdek, Zsolt Lángi
We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained…
Remarks on soft ball packings in dimensions 2 and 3
Károly Bezdek, Zsolt Lángi
We study translative arrangements of centrally symmetric convex domains in the plane (resp., of congruent balls in the Euclidean -space) that neither pack nor cover. We define t…