On the visibility graph of convex translates

We show that the visibility graph of a set of non-intersecting translates o f the same compact convex object in R-2 always contains a Hamiltonian path. Furthermore, we show that every other edge in the Hamiltonian path can be used to obtain a perfect matching that is realized by a set of non-intersec ting lines of sight. (C) 2001 Elsevier Science B.V. All rights reserved.