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Rigidity matroid
In the mathematics of structural rigidity, a rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with rigid edges of fixed lengths, embedded into Euclidean space. In a rigidity matroid for a graph with n vertices in d-dimensional space, a set of edges that defines a subgraph with k degrees of freedom has matroid rank dn − k. A set of edges is independent if and only if, for every edge in the set, removing the edge would increase the number of degrees of freedom of the remaining subgraph.[1][2][3]
- ^ Graver, Jack E. (1991), "Rigidity matroids", SIAM Journal on Discrete Mathematics, 4 (3): 355–368, doi:10.1137/0404032, MR 1105942.
- ^ Whiteley, Walter (1992), "Matroids and rigid structures", Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40, Cambridge: Cambridge Univ. Press, pp. 1–53, doi:10.1017/CBO9780511662041.002, ISBN 978-0-521-38165-9, MR 1165538.
- ^ Whiteley, Walter (1996), "Some matroids from discrete applied geometry", Matroid theory (Seattle, WA, 1995), Contemporary Mathematics, vol. 197, Providence, RI: American Mathematical Society, pp. 171–311, doi:10.1090/conm/197/02540, ISBN 978-0-8218-0508-4, MR 1411692.
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