Abstract
Let G = (V, E) be a graph and x, y, z ∈ V be three designated vertices. We give a necessary and sufficient condition for the existence of a rigid two-dimensional framework (G, p), in which x, y, z are collinear. This result extends a classical result of Laman on the existence of a rigid framework on G. Our proof leads to an efficient algorithm which can test whether G satisfies the condition.
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Supported by the MTA-ELTE Egerváry Research Group on Combinatorial Optimization, and the Hungarian Scientific Research Fund grant no. F034930, T037547, and FKFP grant no. 0143/2001.
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Jackson, B., Jordán, T. Rigid Two-Dimensional Frameworks with Three Collinear Points. Graphs and Combinatorics 21, 427–444 (2005). https://doi.org/10.1007/s00373-005-0629-9
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DOI: https://doi.org/10.1007/s00373-005-0629-9