Flexible placements of graphs with rotational symmetry

Sean Dewar; Georg Grasegger; Jan Legerský

doi:10.1007/978-3-030-91352-6_9

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arXiv · 2003.09328

Flexible placements of graphs with rotational symmetry

Sean Dewar·Georg Grasegger·Jan Legerský

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Abstract

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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BibTeX RIS

Sean Dewar, Georg Grasegger, Jan Legerský. 2020-03-20. Flexible placements of graphs with rotational symmetry. https://doi.org/10.1007/978-3-030-91352-6_9

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