2015/07/17 by Martin Nöllenburg, Roman Prutkin, Ignaz Rutter · 1 citation
Computer Science · #Computational Geometry and Mesh Generation #Cellular Automata and Applications #Advanced Graph Theory Research
paper · doi:10.20382/jocg.v7i1a3
openalex publication_date 2015/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
An st-path in a drawing of a graph is self-approaching if during the traversal of the corresponding curve from s to any point t' on the curve the distance to t' is non-increasing. A path has increasing chords if it is self-approaching in both directions. A drawing is self-approaching (increasing-chord) if any pair of vertices is connected by a self-approaching (increasing-chord) path. We study self-approaching and increasing-chord drawings of triangulations and 3-connected planar graphs. We show that in the Euclidean plane, triangulations admit increasing-chord drawings, and for planar 3-trees we can ensure planarity. We prove that strongly monotone (and thus increasing-chord) drawings of trees and binary cactuses require exponential resolution in the worst case, answering an open question by Kindermann et al. (GD 2014). Moreover, we provide a binary cactus that does not admit a self-approaching drawing. Finally, we show that 3-connected planar graphs admit increasing-chord drawings in the hyperbolic plane and characterize the trees that admit such drawings.