Linking \((n-2)\)-dimensional panels in \(n\)-space. I: \((k-1,k)\)-graphs and \((k-1,k)\)-frames
An \((m,k)\)-graph is a graph satisfying \(f\leq mu-k\) for each subset of \(f\) edges on \(u\) nodes where \(u\) is sufficiently large, and with equality when \(f\) is the number of edges of the graph. A \((k-1,k)\)-frame is a structure generalizing an \((n-2,2)\)-framework in \(n\)-spaces, a structure consisting of a finite set of \((n-2)\)-dimensional panels in \(n\)-spaces and a set of rigid bars each joining a pair of panels using ball joints. The author proves that a graph is the underlying graph of an isostatic \((k-1,k)\)-frame if and only if it is a \((k-1,k)\)-graph.
scientific article; zbMATH DE number 25817