On Generic Rigidity in the Plane

1982 ◽  
Vol 3 (1) ◽  
pp. 91-98 ◽  
Author(s):  
L. Lovász ◽  
Y. Yemini
Keyword(s):  
Generic Rigidity

Generic Rigidity Percolation: The Pebble Game

1995 ◽  
Vol 75 (22) ◽  
pp. 4051-4054 ◽  
Author(s):  
D. J. Jacobs ◽  
M. F. Thorpe
Keyword(s):  
Rigidity Percolation ◽  
Generic Rigidity ◽  
Pebble Game

Generic Rigidity of Network Glasses

2005 ◽  
pp. 239-277 ◽  
Author(s):  
M.F. Thorpe ◽  
D.J. Jacobs ◽  
N.V. Chubynsky ◽  
A.J. Rader
Keyword(s):  
Generic Rigidity ◽  
Network Glasses

Generic rigidity of protein frameworks

2000 ◽  
Vol 18 (4-5) ◽  
pp. 557
Author(s):  
Walter Whiteley ◽  
Joy Abramson ◽  
Marcus Emmanuel Barnes ◽  
Lisa Young
Keyword(s):  
Generic Rigidity

scholarly journals Which graphs are rigid in $$\ell _p^d$$?

2021 ◽  
Author(s):  
Sean Dewar ◽  
Derek Kitson ◽  
Anthony Nixon
Keyword(s):  
Projective Plane ◽  
General Class ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Sparse Graph ◽  
Normed Spaces ◽  
3 Dimensional ◽  
Strictly Convex ◽  
Generic Rigidity

AbstractWe present three results which support the conjecture that a graph is minimally rigid in d-dimensional $$\ell _p$$ ℓ p -space, where $$p\in (1,\infty )$$ p ∈ ( 1 , ∞ ) and $$p\not =2$$ p ≠ 2 , if and only if it is (d, d)-tight. Firstly, we introduce a graph bracing operation which preserves independence in the generic rigidity matroid when passing from $$\ell _p^d$$ ℓ p d to $$\ell _p^{d+1}$$ ℓ p d + 1 . We then prove that every (d, d)-sparse graph with minimum degree at most $$d+1$$ d + 1 and maximum degree at most $$d+2$$ d + 2 is independent in $$\ell _p^d$$ ℓ p d . Finally, we prove that every triangulation of the projective plane is minimally rigid in $$\ell _p^3$$ ℓ p 3 . A catalogue of rigidity preserving graph moves is also provided for the more general class of strictly convex and smooth normed spaces and we show that every triangulation of the sphere is independent for 3-dimensional spaces in this class.

Sign in / Sign up

Export Citation Format

Share Document