• DOI:10.1145/513400.513404
Corpus ID: 14257671

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

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