Flexible placements of graphs with rotational symmetry
Johann Radon Institute for Computational and Applied Mathematics (RICAM)（约翰·拉德诺计算与应用数学研究所）；Austrian Academy of Sciences（奥地利科学院）；Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）；Research Institute for Symbolic Computation (RISC)（符号计算研究所）；Czech Technical University in Prague（布拉格捷克理工大学）
英文摘要：
We study the existence of an $n$-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.
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