Untangling Graphs on Surfaces

Orateur : Loïc Dubois
23 Avril 2024 à 14:00 ; lieu : Salle de séminaire 4B125 (bâtiment Copernic)

Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide a polynomial time algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices and edges of the graph on the surface (avoiding the obstacles) to remove all crossings; in other words, whether the drawing is homotopic to an embedding. While the problem boils down to planarity testing when the surface is the sphere or the disk (or equivalently the plane without any obstacle), the other cases have never been studied before, except when the input graph is a cycle, in an abundant literature in topology and more recently by Despré and Lazarus [SoCG 2017, J. ACM 2019].


Salle de séminaire 4B125 (bâtiment Copernic)

5 Boulevard Descartes 77420 Champs-sur-Marne