Anthony Genevois

activity

20242026

collaborators

12 papers

math.CO2026

A median degree from crossing graphs of median graphs

Anthony Genevois

The crossing graph $Cross (M)$ of a median graph $M$ is defined as the graph whose vertices are the $Θ$ -classes of $M$ and whose edges connect two $Θ$ -classes whenever they…

math.CO2026

Cell structure of mediangle graphs

Victor Chepoi, Anthony Genevois, Kolja Knauer

Mediangle graphs are a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems). Answering a question moti…

math.GR2026

Polynomial hyperbolicity and products of free groups

Anthony Genevois

In this article, we define a locally finite graph $X$ as $I^\cdot$ -polynomially hyperbolic if there exists a Lipschitz map $I ¨ : X \to Z$ to some hyperbolic space $Z$ satisfying the foll…

math.GR2026

Relative numbers of ends and quasi-median graphs

Anthony Genevois

Given a finitely generated $G$ and a subgraph $H \leq G$ , the relative number of ends $e (G, H)$ is the number of ends of a Schreier graph $Sch (G, H)$ and the number of coend…

math.GR2026

Virtual splittings of right-angled Artin groups

Oussama Bensaid, Anthony Genevois, Romain Tessera

In this article, we determine, given a finite graph $I^$ and an integer $n \geq 1$ , when a right-angled Artin group $A (I^)$ virtually splits over an abelian subgroup of rank $n$ . M…

math.GR2026

Coarse separation and splittings in right-angled Artin groups

Oussama Bensaid, Anthony Genevois, Romain Tessera

In this article, we characterise geometrically when a right-angled Artin group splits over an abelian subgroup. More precisely, given a finite graph $I^$ , we show that $A (I^)$ spli…