Theorem G can be realized as an infinitesimally rigid panel-hinge framework if and only if 5G contains six-edge-disjoint spanning trees.
{"Image DocumentName": "TheoremG can be realized as an infinitesimally rigid panel-hinge framework if and only if 5G contains six-edge-disjoint spanning trees.", "Image ImageDescription": "Def. G is a k-graph if def(G)=k; it is a minimal k-graph if def(G)=k and removal of any edge results in a non k-graph. Theorem: If G is a minimal k-graph, then it can be realized as a panel-hinge framework with k degree of freedom. (Outline) combinatorial part\uff1a propose an inductive construction of minimal k-graphs w.r.t. # vertices. algebraic part\uff1aprovide an explicit construction of a k-dof panel-hinge framework (G,p) following the inductive construction given in combinatorial part.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}