4 papers
Strictly convex drawings of planar graphs
Imre Barany, Guenter Rote
Every three-connected planar graph with n vertices has a drawing on an O(n^2) x O(n^2) grid in which all faces are strictly convex polygons. These drawings are obtained by perturbi…
On the geometric dilation of closed curves, graphs, and point sets
Adrian Dumitrescu, Annette Ebbers-Baumann, Ansgar Grüne +2
The detour between two points u and v (on edges or vertices) of an embedded planar graph whose edges are curves is the ratio between the shortest path in in the graph between u and…
Non-crossing frameworks with non-crossing reciprocals
David Orden, Guenter Rote, Francisco Santos +3
We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-…
Planar Minimally Rigid Graphs and Pseudo-Triangulations
Ruth Haas, David Orden, Guenter Rote +6
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees. In this paper we prove th…