Covering convex sets with non-overlapping polygons Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Robison, Arch Shen, Xiao 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. Elsevier 1990 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/4065 Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. 1990;81(2):153-164. doi:<a href="https://doi.org/10.1016/0012-365X(90)90147-A">10.1016/0012-365X(90)90147-A</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/0012-365X(90)90147-A info:eu-repo/semantics/altIdentifier/issn/0012-365X info:eu-repo/semantics/altIdentifier/e-issn/1872-681X info:eu-repo/semantics/closedAccess