Connected rigidity matroids and unique realizations of graphs
A graph is shown to have a unique realization in the plane if and only if it is 3-connected and redundantly rigid, resolving the last open case of a conjecture by \textit{B. Hendrickson} [SIAM J. Comput. 21, 65--84 (1992; Zbl 0756.05047)]. One key ingredient for the proof is the fact that 2-rigidity leads to a finer decomposition of the rigidity matroid than the one pointed out by \textit{B. Servatius} [SIAM J. Discrete Math. 2, 582--589 (1989; Zbl 0723.05034)], another is the new characterization of M-circuits by \textit{A. Berg} and \textit{T. Jordán} [J. Comb. Theory, Ser. B 88, 77--97 (2003; Zbl 1036.05047)].
scientific article; zbMATH DE number 2165067
scientific article