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.
References
Primary source
James Cruickshank, Sean Dewar and Derek Kitson, “Algebraic connectivity in normed spaces”, arXiv:2508.00134 (2025).
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