Sufficient connectivity conditions for rigidity of symmetric frameworks
classification
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connectivityrigiditysufficientsymmetricconditionsplaneconnectedfamous
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It is a famous result of Lovasz and Yemini (1982) that 6-connected graphs are rigid in the plane. This was recently improved by Jackson and Jordan (2009) who showed that 6-mixed connectivity is also sufficient for rigidity. Here we give sufficient graph connectivity conditions for both `forced symmetric' and `incidentally symmetric' infinitesimal rigidity in the plane.
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