On the number of embeddings of minimally rigid graphs

@inproceedings{Borcea2002OnTN,
  title={On the number of embeddings of minimally rigid graphs},
  author={C. Borcea and I. Streinu},
  booktitle={SCG '02},
  year={2002}
}
  • C. Borcea, I. Streinu
  • Published in SCG '02 2002
  • Mathematics, Computer Science
  • (MATH) Rigid frameworks in some Euclidian space are embedded graphs having a unique local realization (up to Euclidian motions) for the given edge lengths, although globally they may have several. We study first the number of distinct planar embeddings of rigid graphs with n vertices. We show that, modulo planar rigid motions, this number is at most $2n-4\choose n-2 \approx 4n. We also exhibit several families which realize lower bounds of the order of 2n, 2.21n and 2.88n.(MATH) For the upper… CONTINUE READING
    46 Citations

    Figures and Topics from this paper

    On the maximal number of real embeddings of minimally rigid graphs in R2, R3 and S2
    • 3
    • Highly Influenced
    • PDF
    Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs
    • 13
    • Highly Influenced
    • PDF
    Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs
    • 7
    • PDF
    On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs
    • 4
    • PDF
    Counting Euclidean embeddings of rigid graphs
    • 5
    • PDF
    New upper bounds for the number of embeddings of minimally rigid graphs.
    • PDF
    A G ] 1 2 Ju l 2 00 2 Point Configurations and Cayley-Menger Varieties
    Lower Bounds on the Number of Realizations of Rigid Graphs
    • 7
    • Highly Influenced
    • PDF
    Equivalent Realisations of a Rigid Graph Bill Jackson
    • Highly Influenced
    An upper bound on Euclidean embeddings of rigid graphs with 8 vertices
    • 2
    • PDF

    References

    SHOWING 1-6 OF 6 REFERENCES
    On the topology of real algebraic surfaces, Izv
    • Akad. Nauk SSSR
    • 1949
    Cinderella, an interactive software package for Geometry
    • 1999
    Cinderella
    • an interactive software package for Geometry, Springer Verlag
    • 1999
    and U
    • Kortenkamp, Cinderella, an Interactive Software Package for Geometry, Springer-Verlag, New York,
    • 1999
    Embedability of weighted graphs in k-space is strongly NP-hard, Proc
    • Allerton Conf. on Communications, Control and Computing,
    • 1979
    and H
    • Rademacher, Vorlesungen über die Theorie der Polyedern, Springer-Verlag, Berlin,
    • 1934