Tensegrity frameworks in one-dimensional space

The edge set of a graph G is partitioned into two subsets E C ∪ E S . A tensegrity framework with underlying graph G and with cables for E C and struts for E S is proved to be rigidly embeddable into a one-dimensional line if and only if G is 2-edge-connected and every 2-vertex-connected component of G intersects both E C and E S . Polynomial algorithms are given for finding an embedding of such graphs and for checking the rigidity of a given one-dimensional embedding.