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Abstract
We study the existence of ann-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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Acknowledgments
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 675789. The project was supported by the Austrian Science Fund (FWF): P31061, P31888 and W1214-N15, and by the Ministry of Education, Youth and Sports of the Czech Republic, project no. CZ.02.1.01/0.0/ 0.0/16_019/0000778.
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Authors and Affiliations
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria
Sean Dewar & Georg Grasegger
Johannes Kepler University Linz, Research Institute for Symbolic Computation, Linz, Austria
Jan Legerský
Department of Applied Mathematics, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czechia
Jan Legerský
- Sean Dewar
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Correspondence toSean Dewar.
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Department of Engineering, Manchester Metropolitan University, Manchester, UK
William Holderbaum
School of Engineering, London South Bank University, London, UK
J. M. Selig
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Dewar, S., Grasegger, G., Legerský, J. (2022). Flexible Placements of Graphs with Rotational Symmetry. In: Holderbaum, W., Selig, J.M. (eds) 2nd IMA Conference on Mathematics of Robotics. IMA 2020. Springer Proceedings in Advanced Robotics, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-91352-6_9
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