zbMath0877.52001MaRDI QIDQ2564763
Horst Martini, Petru Soltan, Vladimir G. Boltyanski
Publication date: 16 January 1997
Published in: Universitext (Search for Journal in Brave)
Projections and angle sums of belt polytopes and permutohedra ⋮
Complete sets in normed linear spaces ⋮
On the partition of plane sets into 6 subsets of small diameter ⋮
Lower bound on the minimum number of edges in subgraphs of Johnson graphs ⋮
Estimations of covering functionals of simplices ⋮
On Boltyanski and Gohberg's partition conjecture ⋮
Improved bounds for Hadwiger's covering problem via thin-shell estimates ⋮
Helly-type theorems for homothets of planar convex curves ⋮
Borsuk's partition problem in ℓₚ⁴ ⋮
Duality of gauges and symplectic forms in vector spaces ⋮
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Covering functionals of cones and double cones ⋮
Covering the boundary of a convex body with its smaller homothetic copies ⋮
Independence numbers of random subgraphs of a distance graph ⋮
Behaviour of inradius, circumradius, and diameter in generalized Minkowski spaces ⋮
Minkowski Geometry—Some Concepts and Recent Developments ⋮
Some properties of geodesic semi E-b-vex functions ⋮
On a convex operator for finite sets ⋮
New algorithms for \(k\)-center and extensions ⋮
On the number of edges in induced subgraphs of a special distance graph ⋮
Independence numbers of random subgraphs of distance graphs ⋮
On the minimal number of edges in induced subgraphs of special distance graphs ⋮
A new estimate for the number of edges in induced subgraphs of a special distance graph ⋮
On the covering index of convex bodies ⋮
Detecting fixed points of nonexpansive maps by illuminating the unit ball ⋮
Covering functionals of convex polytopes with few vertices ⋮
Continuity properties of the ball hull mapping ⋮
Covering convex hulls of compact convex sets with smaller homothetic copies ⋮
Monotone path-connectedness of strict suns ⋮
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On the Carathéodory number for strong convexity ⋮
Diametrically complete sets in Minkowski spaces ⋮
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On geodesic \(E\)-convex sets, geodesic \(E\)-convex functions and \(E\)-epigraphs ⋮
Diameters of random distance graphs ⋮
On the maximal number of edges in a uniform hypergraph with one forbidden intersection ⋮
On threshold probabilities for the realization of a random graph by a geometric graph ⋮
Unnamed Item ⋮
On Ramsey Type Problems in Combinatorial Geometry ⋮
Estimate of the number of edges in special subgraphs of a distance graph ⋮
Ball polytopes and the Vázsonyi problem ⋮
A quantitative program for Hadwiger's covering conjecture ⋮
Ball and spindle convexity with respect to a convex body ⋮
Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. ⋮
No dimension-independent core-sets for containment under homothetics ⋮
Unique metric segments in the hyperspace over a strictly convex Minkowski space ⋮
Counterexamples to Borsuk's conjecture on spheres of small radius ⋮
HILBERT TRANSFORMS ALONG LIPSCHITZ DIRECTION FIELDS: A LACUNARY MODEL ⋮
Minimum Manhattan network problem in normed planes with polygonal balls: a factor 2.5 approximation algorithm ⋮
Minkowski addition of \(H\)-convex sets and related Helly-type theorems. ⋮
Covering unit spheres and balls of normed spaces by smaller balls ⋮
A branch-and-bound approach for estimating covering functionals of convex bodies ⋮
Geometry where direction matters -- or does it? ⋮
Starshaped sets ⋮
New lower bounds for the independence numbers of distance graphs with vertices in \(\{-1,0,1\}^{n}\) ⋮
Illuminating and covering convex bodies ⋮
On translative coverings of convex bodies ⋮
Some analogues of the Borsuk problem in \(\mathbb Q^{n}\) ⋮
Realization of subgraphs of random graphs by graphs of diameters in Euclidean spaces ⋮
On independence numbers of distance graphs with vertices in \(\{-1,0,1\}^n\): estimates, conjectures, and applications to the Nelson-Erdős-hadwiger problem and the borsuk problem ⋮
Covering functionals of Minkowski sums and direct sums of convex bodies ⋮
Independence numbers and chromatic numbers of random subgraphs in some sequences of graphs ⋮
Separation in totally-sewn 4-polytopes with the decreasing universal edge property ⋮
On stability of the independence number of a certain distance graph ⋮
Minsum location extended to gauges and to convex sets ⋮
Semi-inner products and the concept of semi-polarity ⋮
Shape from Silhouettes in Discrete Space ⋮
Homothetic covering of convex hulls of compact convex sets ⋮
Characterizations of \(l_\infty^n\) and \(l_1^n\), and their stabilities ⋮
Convex values and Lipschitz behavior of the complete hull mapping ⋮
Carathéodory's theorem and \(H\)-convexity ⋮
Covering functionals of convex polytopes ⋮
One problem on geometric Ramsey numbers ⋮
Antipodality properties of finite sets in Euclidean space ⋮
On the multiple Borsuk numbers of sets ⋮
Minsum hyperspheres in normed spaces ⋮
The Borsuk partition problem: the seventieth anniversary ⋮
Covering a convex body vs. covering the set of its extreme points ⋮
On parallel packing and covering of squares and cubes ⋮
On threshold probability for the stability of independent sets in distance graphs ⋮
Cube is a strict local maximizer for the illumination number ⋮
Preservation of approximative properties of Chebyshev sets and suns in a plane ⋮
On covering functionals of convex bodies ⋮
Partition bounded sets into sets having smaller diameters ⋮
Constructions of maximum few-distance sets in Euclidean spaces ⋮
Around Borsuk's hypothesis ⋮
Unnamed Item ⋮
On the realization of subgraphs of a random graph by diameter graphs in Euclidean spaces ⋮
Hamiltonian paths in distance graphs ⋮
The Fermat--Torricelli problem in normed planes and spaces ⋮
The number of edges in induced subgraphs of some distance graphs ⋮
New Turán type bounds for Johnson graphs ⋮
On regular 4-coverings and their application for lattice coverings in normed planes ⋮
Blocking numbers and fixing numbers of convex bodies ⋮
Discrete Geometry in Minkowski Spaces ⋮
Problems on discrete metric spaces ⋮
Each convex body in \(E^3\) symmetric about a plane can be illuminated by 8 directions ⋮
On convex partitions of polygonal regions ⋮
The geometry of Minkowski spaces -- a survey. II. ⋮
New Algorithms for k-Center and Extensions ⋮
Counterexamples to Borsuk's conjecture with large girth ⋮
Borsuk's problem and the chromatic numbers of metric spaces ⋮
On the illumination of a class of convex bodies ⋮
Covering by homothets and illuminating convex bodies ⋮
Lipschitz selections of set-valued mappings and Helly's theorem ⋮
On geodesic strongly \(E\)-convex sets and geodesic strongly \(E\)-convex functions