20 citations · 169 across the 52 of their papers we have counts for
8 papers · 1 filter
The geometry of flip graphs and mapping class groups
Valentina Disarlo, Hugo Parlier
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called fli…
Chromatic numbers of hyperbolic surfaces
Hugo Parlier, Camille Petit
This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the -chromatic number is the minimum number of colors needed to color the points of the space…
Curve graphs on surfaces of infinite type
Ariadna Fossas, Hugo Parlier
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves whic…
The genus of curve, pants and flip graphs
Hugo Parlier, Bram Petri
This article is about the graph genus of certain well studied graphs in surface theory: the curve, pants and flip graphs. We study both the genus of these graphs and the genus of t…
Injective maps between flip graphs
Javier Aramayona, Thomas Koberda, Hugo Parlier
We prove that every injective simplicial map between flip graphs is induced by a subsurface inclusion , except in finitely many cases.…
Systoles and kissing numbers of finite area hyperbolic surfaces
Federica Fanoni, Hugo Parlier
We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface…