@article{4065, abstract = {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.}, author = {Edelsbrunner, Herbert and Robison, Arch and Shen, Xiao}, issn = {1872-681X}, journal = {Discrete Mathematics}, number = {2}, pages = {153 -- 164}, publisher = {Elsevier}, title = {{Covering convex sets with non-overlapping polygons}}, doi = {10.1016/0012-365X(90)90147-A}, volume = {81}, year = {1990}, }