The edge-redundant rigidity conjecture for complete graphs in
The edge-redundant rigidity conjecture for complete graphs in
Let , let , and let denote the complete graph on vertices. A graph is edge-redundantly rigid in a normed space if it has a framework that is infinitesimally rigid and remains infinitesimally rigid after deleting any edge. Edge-redundant rigidity conjecture. For every and every , the complete graph is edge-redundantly rigid in .
The preceding proposition rules out , so the conjecture asserts that the stated threshold is sufficient as well as necessary. The supplied excerpt gives no evidence that the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
James Cruickshank, Sean Dewar and Derek Kitson, “Algebraic connectivity in normed spaces”, arXiv:2508.00134 (2025).
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