Mutually contiguous translates of a plane disk (Q1896007)

The authors consider topological disks (i.e. homeomorphic to the unit circle) in the euclidean plane \(E^2\). Two disks are called contiguous, if they have a common point but do not overlap. Their main result is: If \(n\) translates of a disk are mutually contiguous, then \(n \leq 4\). As the authors point out, this answers a question posed by J. Mitchell in 1991. Further several related results are given.