A necessary condition for generic rigidity of bar-and-joint frameworks in dspace

  title={A necessary condition for generic rigidity of bar-and-joint frameworks in dspace},
  author={Bill Jackson},
A graph G = (V,E) is d-sparse if each subset X ⊆ V with |X| ≥ d induces at most d|X| − ( d+1 2 ) edges in G. Laman showed in 1970 that a necessary and sufficient condition for a realisation of G as a generic bar-and-joint framework in R to be rigid is that G should have a 2sparse subgraph with 2|V | − 3 edges. Although Laman’s theorem does not hold when d ≥ 3, Cheng and Sitharam recently showed that if G is generically rigid in R then every maximal 3-sparse subgraph of G must have 3|V | − 6… CONTINUE READING

From This Paper

Topics from this paper.


Publications citing this paper.


Publications referenced by this paper.
Showing 1-6 of 6 references

Generalizations of Kempes Universality Theorem

  • T. G. Abbot
  • MSc thesis,
  • 2008
1 Excerpt

Some matroids from discrete applied geometry, in Matroid

  • W. Whiteley
  • Contemp. Math.,
  • 1996
1 Excerpt

On generic rigidity in the plane

  • L. Lovász, Y. Yemini
  • SIAM J. Algebraic Discrete Methods,
  • 1982
2 Excerpts

On graphs and rigidity of plane skeletal structures

  • G. Laman
  • J. Engineering Math.,
  • 1970
1 Excerpt

On the calculation of the equilibrium and stiffness of frames

  • J. C. Maxwell
  • Philosophical Magazine
  • 1864

Similar Papers

Loading similar papers…