Mixed volume techniques for embeddings of Laman graphs

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.

• Type: Journal
• Year: 2010
• Where: COMGEO
• Authors: Reinhard Steffens, Thorsten Theobald
• Keywords: Applied Computing, Combinatorial Bounds, COMGEO 2010, Edge Length Constraints, Modulo Rigid Motions