Constructing reflection-symmetric flexible realisations of graphs
Combinatorics
2025-12-11 v1
Abstract
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with reflection-symmetric flexible realisations. This condition is based on a specific type of edge colouring, where edges are assigned one of three colours in a symmetric way. From some of these colourings we also construct concrete reflection-symmetric realisations with their corresponding symmetry preserving motion. We study also a specific class of reflection-symmetric realisations consisting of triangles and parallelograms.
Cite
@article{arxiv.2408.06928,
title = {Constructing reflection-symmetric flexible realisations of graphs},
author = {Sean Dewar and Georg Grasegger and Jan Legerský},
journal= {arXiv preprint arXiv:2408.06928},
year = {2025}
}