Yayın: A necessary condition for generic rigidity of bar‐and‐joint frameworks in d‐space
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AbstractA graph is ‐sparse if each subset with induces at most edges in . Maxwell showed in 1864 that a necessary condition for a generic bar‐and‐joint framework with at least vertices to be rigid in is that should have a ‐sparse subgraph with edges. This necessary condition is also sufficient when but not when . Cheng and Sitharam strengthened Maxwell's condition by showing thateverymaximal ‐sparse subgraph of should have edges when . We extend their result to all .
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Wiley
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rigidity matroid, Graph representations (geometric and intersection representations, etc.), C25, 05C62, 70B15, Combinatorial aspects of matroids and geometric lattices, Planar graphs, geometric and topological aspects of graph theory, infinitesimal rigidity, Rigidity and flexibility of structures (aspects of discrete geometry), FOS: Mathematics, bar-joint framework, Mathematics - Combinatorics, Combinatorics (math.CO)