2024/08/13 by Dewar, Sean, Grasegger, Georg, Legerský, Jan
#05C70 #52C25 #70B15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.06928
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.