9 papers
Disjoint faces in simple drawings of the complete graph and topological Heilbronn problems
Alfredo Hubard, Andrew Suk
Given a complete simple topological graph , a -face generated by is the open bounded region enclosed by the edges of a non-self-intersecting -cycle in . Interesting…
Short Topological Decompositions of Non-Orientable Surfaces
Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay
In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm t…
Equipartitions and Mahler volumes of symmetric convex bodies
Matthieu Fradelizi, Alfredo Hubard, Mathieu Meyer +2
Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular,…
Random polytopes and the wet part for arbitrary probability distributions
Imre Bárány, Matthieu Fradelizi, Xavier Goaoc +2
We examine how the measure and the number of vertices of the convex hull of a random sample of points from an arbitrary probability measure in relates to the wet…
Limits of Order Types
Xavier Goaoc, Alfredo Hubard, Rémi de Joannis de Verclos +2
We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obta…
Bisecting measures with hyperplane arrangements
Alfredo Hubard, Roman Karasev
We show that when is a power of two, any measures in can be bisected by an arrangement of hyperplanes.