21 citations · 64 across the 25 of their papers we have counts for
18 papers · 1 filter
Box complexes: at the crossroad of graph theory and topology
Hamid Reza Daneshpajouh, Frédéric Meunier
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bou…
Colorings of complements of line graphs
Hamid Reza Daneshpajouh, Frédéric Meunier, Guilhem Mizrahi
Our purpose is to show that complements of line graphs enjoy nice coloring properties. We show that for all graphs in this class the local and usual chromatic numbers are equal. We…
Topological bounds for graph representations over any field
Meysam Alishahi, Frédéric Meunier
Haviv ({\em European Journal of Combinatorics}, 2019) has recently proved that some topological lower bounds on the chromatic number of graphs are also lower bounds on their orthog…
Different versions of the nerve theorem and rainbow simplices
Frédéric Meunier, Luis Montejano
Given a simplicial complex and a collection of subcomplexes covering it, the nerve theorem, a fundamental tool in topological combinatorics, guarantees a certain connectivity of th…
Envy-free cake division without assuming the players prefer nonempty pieces
Frédéric Meunier, Shira Zerbib
Consider players having preferences over the connected pieces of a cake, identified with the interval . A classical theorem, found independently by Stromquist and by Woo…
Multilabeled versions of Sperner's and Fan's lemmas and applications
Frédéric Meunier, Francis Edward Su
We propose a general technique related to the polytopal Sperner lemma for proving old and new multilabeled versions of Sperner's lemma. A notable application of this technique yiel…
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
Jesus A. De Loera, Xavier Goaoc, Frédéric Meunier +1
We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We…
Fair splitting of colored paths
Meysam Alishahi, Frédéric Meunier
This paper deals with two problems about splitting fairly a path with colored vertices, where "fairly" means that each part contains almost the same amount of vertices in each colo…
Achieving rental harmony with a secretive roommate
Florian Frick, Kelsey Houston-Edwards, Frédéric Meunier
Given the subjective preferences of n roommates in an n-bedroom apartment, one can use Sperner's lemma to find a division of the rent such that each roommate is content with a dist…
A business dinner problem
Alejandra Estanislao, Frédéric Meunier
We are given suppliers and customers, and a set of tables. Every evening of the forthcoming days, there will be a dinner. Each customer must eat with each supplier exactly once, bu…
Strengthening topological colorful results for graphs
Meysam Alishahi, Hossein Hajiabolhassan, Frédéric Meunier
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number…
Hedetniemi's conjecture for Kneser hypergraphs
Hossein Hajiabolhassan, Frédéric Meunier
One of the most famous conjecture in graph theory is Hedetniemi's conjecture stating that the chromatic number of the categorical product of graphs is the minimum of their chromati…
Colorful hypergraphs in Kneser hypergraphs
Frédéric Meunier
Using a -generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite g…
A combinatorial approach to colourful simplicial depth
Antoine Deza, Frédéric Meunier, Pauline Sarrabezolles
The colourful simplicial depth conjecture states that any point in the convex hull of each of d+1 sets, or colours, of d+1 points in general position in R^d is contained in at leas…
The chromatic number of almost stable Kneser hypergraphs
Frédéric Meunier
Let be the set of -subsets of such that for all , we have We define almost -stable Kneser hypergraph $KG^r{{[n]}\choose k}_{s{\ti…
Completely symmetric configurations for sigma-games on grid graphs
Mathieu Florence, Frédéric Meunier
The paper deals with sigma-games on grid graphs (in dimension 2 and more) and conditions under which any completely symmetric configuration of lit vertices can be reached -- in par…
Polytopal complexes: maps, chain complexes and... necklaces
Frédéric Meunier
The notion of polytopal map between two polytopal complexes is defined. Surprisingly, this definition is quite simple and extends naturally those of simplicial and cubical maps. It…
Carathéodory, Helly and the others in the max-plus world
Stéphane Gaubert, Frédéric Meunier
Carathéodory's, Helly's and Radon's theorems are three basic results in discrete geometry. Their max-plus counterparts have been proved by various authors. In this paper, more adva…