Add to ORKGInternational audienceA line L is a transversal to a family F of convex objects in R^d if it intersects every member of F. In this paper we show that for every integer d>2 there exists a family of 2d-1 pairwise disjoint unit balls in R^d with the property that every subfamily of size 2d-2 admits a transversal, yet any line misses at least one member of the family. This answers a question of Danzer from 1957
http://portal.acm.orgInternational audienceLet S be an ordered set of disjoint unit spheres in R3 We...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
International audienceA line L is a transversal to a family F of convex objects in R^d if it interse...
International audienceWe prove Helly-type theorems for line transversals to disjoint unit balls in $...
A line L is a transversal to a family F of convex objects in R^d if it intersects every member of F....
We prove that the set of directions of lines intersecting three disjoint balls in R3 in a given orde...
AbstractA fresh look is taken at the fractional Helly theorem for line transversals to families of c...
International audienceIt is known that if n>=2d pairwise disjoint balls in R^d have a unique line ℓ ...
International audienceWe prove that the set of directions of lines intersecting three disjoint balls...
Attempts to generalize Helly's theorem to sets of lines intersecting convex sets led to a series of ...
We prove that the maximum number of geometric permutations, induced by line transversals to a collec...
SESSION: Session 8AInternational audienceWe prove that the set of directions of lines intersecting t...
AbstractWe prove that a collection of compact convex sets of bounded diameters in Rd that is unbound...
AbstractWe show that a set of n disjoint unit spheres in Rd admits at most two distinct geometric pe...
http://portal.acm.orgInternational audienceLet S be an ordered set of disjoint unit spheres in R3 We...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
International audienceA line L is a transversal to a family F of convex objects in R^d if it interse...
International audienceWe prove Helly-type theorems for line transversals to disjoint unit balls in $...
A line L is a transversal to a family F of convex objects in R^d if it intersects every member of F....
We prove that the set of directions of lines intersecting three disjoint balls in R3 in a given orde...
AbstractA fresh look is taken at the fractional Helly theorem for line transversals to families of c...
International audienceIt is known that if n>=2d pairwise disjoint balls in R^d have a unique line ℓ ...
International audienceWe prove that the set of directions of lines intersecting three disjoint balls...
Attempts to generalize Helly's theorem to sets of lines intersecting convex sets led to a series of ...
We prove that the maximum number of geometric permutations, induced by line transversals to a collec...
SESSION: Session 8AInternational audienceWe prove that the set of directions of lines intersecting t...
AbstractWe prove that a collection of compact convex sets of bounded diameters in Rd that is unbound...
AbstractWe show that a set of n disjoint unit spheres in Rd admits at most two distinct geometric pe...
http://portal.acm.orgInternational audienceLet S be an ordered set of disjoint unit spheres in R3 We...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...
We show that a set of n disjoint unit spheres in R d admits at most two distinct geometric permutati...