Flexible placements of graphs with rotational symmetry
Combinatorics
2021-11-24 v1 Robotics
Metric Geometry
Abstract
We study the existence of an -fold rotationally symmetric placement of a symmetric graph in the plane allowing a continuous deformation that preserves the symmetry and the distances between adjacent vertices. We show that such a flexible placement exists if and only if the graph has a NAC-colouring satisfying an additional property on the symmetry; a NAC-colouring is a surjective edge colouring by two colours such that every cycle is either monochromatic, or there are at least two edges of each colour.
Keywords
Cite
@article{arxiv.2003.09328,
title = {Flexible placements of graphs with rotational symmetry},
author = {Sean Dewar and Georg Grasegger and Jan Legerský},
journal= {arXiv preprint arXiv:2003.09328},
year = {2021}
}