19 citations · 59 across the 23 of their papers we have counts for
33 papers
Intersection patterns of set systems on manifolds with slowly growing homological shatter functions
Sergey Avvakumov, Marguerite Bin, Xavier Goaoc
A theorem of Matoušek asserts that for any , any set system whose shatter function is enjoys a fractional Helly theorem of order : in the -wise intersection…
An asymptotic rigidity property from the realizability of chirotope extensions
Xavier Goaoc, Arnau Padrol
Let be a finite full-dimensional point configuration in . We show that if a point configuration has the property that all finite chirotopes realizable by addi…
Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization
Jean Cardinal, Xavier Goaoc, Sarah Wajsbrot
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set…
A canonical tree decomposition for order types, and some applications
Mathilde Bouvel, Valentin Féray, Xavier Goaoc +1
We introduce and study a notion of decomposition of planar point sets (or rather of their chirotopes) as trees decorated by smaller chirotopes. This decomposition is based on the c…
The Topology of the set of line Transversals
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that for any set of pairwise disjoint open convex sets in , the connected components of the set of lines intersecting every member of are co…
A colorful Goodman-Pollack-Wenger theorem
Andreas F. Holmsen
Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These co…