5 citations · 6 across the 6 of their papers we have counts for
8 papers
A linear bound for the Colin de Verdière parameter for graphs embedded on surfaces
Camille Lanuel, Francis Lazarus, Rudi Pendavingh
We provide a combinatorial and self-contained proof that for all graphs embedded on a surface , the Colin de Verdière parameter is upper bounded by .
Algorithms for Length Spectra of Combinatorial Tori
Vincent Delecroix, Matthijs Ebbens, Francis Lazarus +1
Consider a weighted, undirected graph cellularly embedded on a topological surface. The function assigning to each free homotopy class of closed curves the length of a shortest cyc…
The Hyperbolic Plane in
Vincent Borrelli, Roland Denis, Francis Lazarus +2
We build an explicit isometric embedding of the hyperbolic plane whose image is relatively compact. Its limit set is a closed curve o…
A Universal Triangulation for Flat Tori
Francis Lazarus, Florent Tallerie
A result due to Burago and Zalgaller (1960, 1995) states that every orientable polyhedral surface, one that is obtained by gluing Euclidean polygons, has an isometric piecewise lin…
Algorithms for Contractibility of Compressed Curves on 3-Manifold Boundaries
Erin Wolf Chambers, Francis Lazarus, Arnaud de Mesmay +1
In this paper we prove that the problem of deciding contractibility of an arbitrary closed curve on the boundary of a 3-manifold is in NP. We emphasize that the manifold and the cu…
Computing the Geometric Intersection Number of Curves
Vincent Despré, Francis Lazarus
The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e. of any curve obtained by continuous deformation.…
Some Triangulated Surfaces without Balanced Splitting
Vincent Despré, Francis Lazarus
Let G be the graph of a triangulated surface of genus . A cycle of G is splitting if it cuts into two components, neither of which is homeomorphic to a disk. A spl…
On the homotopy test on surfaces
Francis Lazarus, Julien Rivaud
Let G be a graph cellularly embedded in a surface S. Given two closed walks c and d in G, we take advantage of the RAM model to describe linear time algorithms to decide if c and d…