# Generic combinatorial rigidity of periodic frameworks

@article{Malestein2013GenericCR, title={Generic combinatorial rigidity of periodic frameworks}, author={Justin Malestein and Louis Theran}, journal={Advances in Mathematics}, year={2013}, volume={233}, pages={291-331} }

Abstract We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks . The characterization is a true analogue of the Maxwell–Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms. To prove our rigidity theorem we introduce and develop periodic direction networks and Z 2 - graded-sparse colored graphs .

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## 56 Citations

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