Generic global rigidity of body-bar frameworks

Journal of Combinatorial Theory. Series B

Volumn 103, Issue 6, 2013, Pages 689-705

  Connelly, R ^a   Jordan T ^b   Whiteley, W ^c  

^a Department of Obstetrics Gynecology   (United States)

^b EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^c YORK UNIVERSITY   (Canada)

Author keywords

Body bar framework; Global rigidity; Redundant rigidity; Rigid graph; Stress matrix

Indexed keywords

EID: 84887616194     PISSN: 00958956     EISSN: 10960902     Source Type: Journal    
DOI: 10.1016/j.jctb.2013.09.002     Document Type: Article

References (32)

1. Aspnes J., Eren T., Goldenberg D.K., Morse A.S., Whiteley W., Yang Y.R., Anderson B.D.O., Belhumeur P.N. A theory of network localization. IEEE Trans. Mob. Comput. 2006, 5(12):1663-1678.
2. Berg A.R., Jordán T. A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid. J. Combin. Theory Ser. B 2003, 88(1):77-97.
3. Connelly R. On generic global rigidity. DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 1991, vol. 4:147-155. AMS.
4. Connelly R. Generic global rigidity. Discrete Comput. Geom. 2005, 33:549-563.
5. Connelly R., Whiteley W. Global rigidity: the effect of coning. Discrete Comput. Geom. 2010, 43(4):717-735.
6. Frank S., Jiang J. New classes of counterexamples to Hendrickson's global rigidity conjecture. Discrete Comput. Geom. 2011, 45(3):574-591.
7. Frank A., Szego L. Constructive characterizations for packing and covering with trees. Discrete Appl. Math. 2003, 131:347-371.
8. Gortler S., Healy A., Thurston D. Characterizing generic global rigidity. Amer. J. Math. August 2010, 132(4):897-939.
9. Gortler S., Thurston D. Characterizing the universal rigidity of generic frameworks arxiv:1001.0172.
10. Hendrickson B. Conditions for unique graph realizations. SIAM J. Comput. 1992, 21:65-84.
11. Jackson B., Jordán T. Connected rigidity matroids and unique realization graphs. J. Combin. Theory Ser. B 2005, 94:1-29.
12. Jackson B., Jordán T. Rigid components in molecular graphs. Algorithmica 2007, 48(4):399-412.
13. Jackson B., Jordán T. Graph theoretic techniques in the analysis of uniquely localizable sensor networks. Localization Algorithms and Strategies for Wireless Sensor Networks 2009, 146-173. IGI Global. G. Mao, B. Fidan (Eds.).
14. Jackson B., Jordán T. Brick partitions of graphs. Discrete Math. 2010, 310(2):270-275.
15. Jackson B., Jordán T. The generic rank of body-bar-and-hinge frameworks. European J. Combin. 2010, 31:574-588.
16. Jackson B., Jordán T., Szabadka Z. Globally linked pairs of vertices in equivalent realizations of graphs. Discrete Comput. Geom. 2006, 35:493-512.
17. Jackson B., Jordán T., Szabadka Z. Globally linked pairs of vertices in rigid frameworks 2013, TR-2012-19, Egerváry Research Group, in press.
18. Katoh N., Tanigawa S. A proof of the molecular conjecture. Discrete Comput. Geom. June 2011, 45(4).
19. Lovász L., Yemini Y. On generic rigidity in the plane. SIAM J. Algebr. Discrete Methods 1982, 3(1):91-98.
20. Nash-Williams C.St.J.A. Edge disjoint spanning trees of finite graphs. J. Lond. Math. Soc. 1961, 36:445-450.
21. Saxe J.B. Embeddability of weighted graphs in k-space is strongly NP-hard 1979, Technical report, Computer Science Department, Carnegie Mellon University.
22. Schrijver A. Combinatorial Optimization 2003, Springer.
23. Szabadka Z. Globally rigid frameworks and rigid tensegrity graphs in the plane 2010, PhD thesis, Eötvös University, Budapest.
24. Tay T.-S. Rigidity of multi-graphs I, linking rigid bodies in n-space. J. Combin. Theory Ser. B 1984, 36:95-112.
25. Tay T.-S. Henneberg's method for bar and body frameworks. Structural Topology 1991, 17:53-58.
26. Tay T.-S., Whiteley W. Recent advances in the generic rigidity of structures. Structural Topology 1984, 9:31-38.
27. Tay T.-S., Whiteley W. Generating isostatic frameworks. Structural Topology 1985, 11:20-69.
28. Tutte W.T. On the problem of decomposing a graph into n connected factors. J. Lond. Math. Soc. 1961, 36:221-230.
29. W. Whiteley, private communication to R. Connelly, March 1982.
30. Whiteley W. Some matroids from discrete applied geometry. Contemp. Math. 1996, vol. 197:171-313. American Mathematical Society. J.E. Bonin, J.G. Oxley, B. Servatius (Eds.).
31. Whiteley W. Rigidity of molecular structures: geometric and generic analysis. Rigidity Theory and Applications 1999, 21-46. Kluwer. M.F. Thorpe, P.M. Duxbury (Eds.).
32. Whiteley W. Counting out the flexibility of molecules. Physical Biology 2005, 2:116-126.