Alfredo Hubard

activity

20102026

most citedConvex Equipartitions: The Spicy Chicken Theorem

48 citations · 91 across the 23 of their papers we have counts for

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14 papers · 1 filter

math.CO2026

Crossing numbers of simplicial complexes

Alfredo Hubard, Cheikh Saliou Ndiaye, Oriol Solé-Pi

This paper studies crossing numbers of $d$ -dimensional simplicial complexes drawn in $R^{2 d}$ or $S^{2 d}$ . We clarify and generalize a number of known results and c…

math.CO2026

Overlap-Helly theorems

Andreas F. Holmsen, Alfredo Hubard

In this paper we introduce a generalization of Helly's theorem closely connected to Bárány-Gromov overlap theorems (also called selection lemmas). Our main result implies both the…

math.CO2025

Crossing numbers of dense graphs on surfaces

Alfredo Hubard, Arnaud de Mesmay, Hugo Parlier

In this paper, we provide upper and lower bounds on the crossing numbers of dense graphs on surfaces, which match up to constant factors. First, we prove that if $G$ is a dense eno…

math.CO2025

Cubulating the sphere with many facets

Sergey Avvakumov, Alfredo Hubard

For each $d \geq 3$ we construct cube complexes homeomorphic to the $d$ -sphere with $n$ vertices in which the number of facets (assuming $d$ constant) is $Ω (n^{5/4})$ . This disprove…

math.CO2024

Bisecting masses with families of parallel hyperplanes

Alfredo Hubard, Pablo Soberón

We prove a common generalization of several mass partition results using hyperplane arrangements to split $R^{d}$ into two sets. Our main result implies the ham sandwich the…

math.CO2024

Crossing lemmas for $k$ -systems of arcs

Alfredo Hubard, Hugo Parlier

We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pair…

math.CO2022

Disjoint faces in simple drawings of the complete graph and topological Heilbronn problems

Alfredo Hubard, Andrew Suk

Given a complete simple topological graph $G$ , a $k$ -face generated by $G$ is the open bounded region enclosed by the edges of a non-self-intersecting $k$ -cycle in $G$ . Interesting…

math.CO2018

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…

math.CO2017★ 1 cited

On a topological version of Pach's overlap theorem

Boris Bukh, Alfredo Hubard

Pach showed that every $d + 1$ sets of points $Q_{1}, \dots, Q_{d + 1} \subset R^{d}$ contain linearly-sized subsets $P_{i} \subset Q_{i}$ such that all the transversal simplices that t…

math.CO2014

Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

Éric Colin de Verdière, Alfredo Hubard, Arnaud de Mesmay

How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial clos…

math.CO2013★ 4 cited

The Erdős-Szekeres problem for non-crossing convex sets

Michael G Dobbins, Andreas F Holmsen, Alfredo Hubard

We show an equivalence between a conjecture of Bisztriczky and Fejes T{ó}th about arrangements of planar convex bodies and a conjecture of Goodman and Pollack about point sets in t…

math.CO2011

Space crossing numbers

Boris Bukh, Alfredo Hubard

We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on…

math.CO2010

Slicing convex sets and measures by a hyperplane

Imre Barany, Alfredo Hubard, Jesus Jeronimo

We generalize the ham sandwich theorem for the case of well separated measures. Given convex bodies $K_{1}, ..., K_{d}$ in $R_{d}$ and numbers $α_{1}, ..., α_{d} \in [0, 1]$ , we give a…