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Mixed volume techniques for embeddings of Laman Graphs

By Reinhard Steffens and Thorsten Theobald


We use Bernstein’s Theorem [1] to obtain combinatorial bounds for the number of embeddings of Laman graph frameworks modulo rigid motions. For this, we study the mixed volume of suitable systems of polynomial equations obtained from the edge length constraints. The bounds can easily be computed and for some classes of graphs, the bounds are tight

Topics: Mixed volume, Laman graphs, minimally rigid graphs, Bernstein’s Theorem
Year: 2013
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