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cs.CG2026
The Hyperbolic Surface Distance, Diameter, and Dirichlet Problems
Vincent Despre, Auguste Gezalyan, Marc Pouget
Despite the prominence of hyperbolic surfaces in mathematics, basic algorithmic questions about them, even computing the distance between two points, have remained open, leaving ma…
cs.CG2025
A Discrete Analog of Tutte's Barycentric Embeddings on Surfaces
Éric Colin de Verdière, Vincent Despré, Loïc Dubois
Tutte's celebrated barycentric embedding theorem describes a natural way to build straight-line embeddings (crossing-free drawings) of a (3-connected) planar graph: map the vertice…
cs.CG2023
Untangling Graphs on Surfaces
Éric Colin de Verdière, Vincent Despré, Loïc Dubois
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawin…