On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
Lenses in arrangements of pseudo-circles and their applications
Journal of the ACM (JACM)
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences
Discrete & Computational Geometry
Intersection reverse sequences and geometric applications
Journal of Combinatorial Theory Series A
On the Union of κ-Round Objects in Three and Four Dimensions
Discrete & Computational Geometry
Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Coloring kk-free intersection graphs of geometric objects in the plane
Proceedings of the twenty-fourth annual symposium on Computational geometry
On the Union of Cylinders in Three Dimensions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On Regular Vertices of the Union of Planar Convex Objects
Discrete & Computational Geometry
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Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only assume that our sets are connected and vertically convex, that is, their intersection with any vertical line is either a segment or the empty set, then the number of tangencies can be superlinear in n, but it cannot exceed n(n log2 n). Our results imply a new upper bound on the number of regular intersection points on the boundary of *C.