Search
Search Results
-
-
-
COUNTEREXAMPLES TO THE COLORFUL TVERBERG CONJECTURE FOR HYPERPLANES
Karasev [16] conjectured that for every set of r blue lines, r green lines, and r red lines in the plane, there exists a partition of them into r ...
-
-
Enclosing Depth and Other Depth Measures
We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of...
-
-
-
Intersecting ellipses induced by a max-sum matching
For an even set of points in the plane, choose a max-sum matching , that is, a perfect matching maximizing the sum of Euclidean distances of its...
-
Tverberg’s Theorem, Disks, and Hamiltonian Cycles
For a finite set of S points in the plane and a graph with vertices on S , consider the disks with diameters induced by the edges. We show that for...
-
Plus Minus Analogues for Affine Tverberg Type Results
The classical 1966 theorem of Tverberg with its numerous variations was and still is a motivating force behind many important developments in convex...
-
Radon numbers and the fractional Helly theorem
A basic measure of the combinatorial complexity of a convexity space is its Radon number. In this paper we answer a question of Kalai, by showing a...
-
Theorems of Carathéodory, Helly, and Tverberg Without Dimension
We initiate the study of no-dimensional versions of classical theorems in convexity. One example is Carathéodory’s theorem without dimension: given...
-
Tverberg-Type Theorems for Matroids: A Counterexample and a Proof
Bárány, Kalai, and Meshulam recently obtained a topological Tverberg-type theorem for matroids, which guarantees multiple coincidences for continuous...
-
Eliminating higher-multiplicity intersections. III. Codimension 2
We study conditions under which a finite simplicial complex K can be mapped to ℝ d without higher-multiplicity intersections. An almost r -embedding is...
-
Algorithms for Radon Partitions with Tolerance
Let P be a set n points in a d-dimensional space. Tverberg theorem says that, if n is at least \((k-1)(d+1)\), then P can be partitioned into k sets...
-
