Connected rigidity matroids and unique realizations of graphs

Journal of Combinatorial Theory. Series B

Volumn 94, Issue 1, 2005, Pages 1-29

  Jackson, Bill ^a   Jordán, Tibor ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15444370051     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jctb.2004.11.002     Document Type: Article

References (24)

1. A. Berg T. Jordán A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid J. Combin. Theory Ser. B 88 2003 77-97
2. A. Berg, T. Jordán, Algorithms for graph rigidity and scene analysis, in: G. Di Battista, U. Zwick (Eds.), Proceedings of the 11th Annual European Symposium on Algorithms (ESA) 2003, Springer Lecture Notes in Computer Science, vol. 2832, 2003, pp. 78-89.
3. R. Connelly Rigidity and energy Invent. Math. 66 1 1982 11-33
4. R. Connelly, On generic global rigidity, applied geometry and discrete mathematics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 4, American Mathematical Society, Providence, RI, 1991, pp. 147-155.
5. R. Connelly, Generic global rigidity, Discrete Comput. Geom., to appear.
6. C.R. Coullard L. Hellerstein Independence and port oracles for matroids with an application to computational learning theory Combinatorica 16 2 1996 189-208
7. G.M. Crippen T.F. Havel Distance Geometry and Molecular Conformation 1988 Wiley New York
8. T. Eren, D. Goldenberg, W. Whiteley, Y.R. Yang, A.S. Morse, B.D.O. Anderson, P.N. Belhumeur, Rigidity, computation, and randomization in network localization, Proceedings of the International Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), March 2004.
9. H. Gluck, Almost all simply connected closed surfaces are rigid, in: Geometric Topology Proceedings of the Conference, Park City, Utah, 1974, Lecture Notes in Mathematics, vol. 438, Springer, Berlin, 1975, pp. 225-239.
10. J. Graver, B. Servatius, H. Servatius, Combinatorial Rigidity, AMS Graduate Studies in Mathematics, vol. 2, American Mathematical Society, Providence, RI, 1993.
11. B. Hendrickson, Conditions for unique graph embeddings, Technical Report 88-950, Department of Computer Science, Cornell University, 1988.
12. B. Hendrickson, The molecule problem: Determining conformation from pairwise distances, Ph.D. Thesis, Department of Computer Science, Cornell University, 1990.
13. B. Hendrickson Conditions for unique graph realizations SIAM J. Comput. 21 1 1992 65-84
14. B. Hendrickson The molecule problem: Exploiting structure in global optimization SIAM J. Optim. 5 1995 835-857
15. L. Henneberg, Die graphische Statik der starren Systeme, Leipzig, 1911.
16. G. Laman On graphs and rigidity of plane skeletal structures J. Eng. Math. 4 1970 331-340
17. L. Lovász Y. Yemini On generic rigidity in the plane SIAM J. Algebraic Discrete Methods 3 1 1982 91-98
18. J.G. Oxley, Matroid Theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1992. xii+532pp.
19. J.B. Saxe, Embeddability of weighted graphs in k-space is strongly NP-hard, Technical Report, Computer Science Department, Carnegie-Mellon University, Pittsburgh, PA, 1979.
20. B. Servatius Birigidity in the plane SIAM J. Discrete Math. 2 4 1989 582-589
21. T.S. Tay W. Whiteley Generating isostatic frameworks Structural Topol. 11 1985 21-69
22. W.T. Tutte, Connectivity in Graphs, University of Toronto Press, 1966.
23. W. Whiteley, Matroids and rigid structures, in: Matroid Applications, Encyclopedia of Mathematical Application, vol. 40, Cambridge University Press, Cambridge, 1992, pp. 1-53.
24. W. Whiteley, Some matroids from discrete applied geometry, in: Matroid Theory (Seattle, WA, 1995), Contemporary Mathematics, vol. 197, American Mathematical Society, Providence, RI, 1996, pp. 171-311.