TY - JOUR AB - We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem. AU - Edelsbrunner, Herbert AU - Robison, Arch AU - Shen, Xiao ID - 4065 IS - 2 JF - Discrete Mathematics SN - 0012-365X TI - Covering convex sets with non-overlapping polygons VL - 81 ER -