Tensegrity frameworks in one-dimensional space

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