Rotational symmetric flexible placements of graphs


We study the existence of an $n$-fold rotational 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.

The 36th European Workshop on Computational Geometry (EuroCG 2020)