On the 3-distortion of a path
<|reference_start|>On the 3-distortion of a path: We prove that, when a path of length n is embedded in R^2, the 3-distortion is an Omega(n^{1/2}), and that, when embedded in R^d, the 3-distortion is an O(n^{1/d-1}).<|reference_end|>
@article{dehornoy2006on,
    title={On the 3-distortion of a path},
    author={Pierre Dehornoy (DMA)},
    journal={European Journal of Combinatorics (2008)
  http://www.elsevier.com/wps/find/journaldescription.cws_home/622824/description#description},
    year={2006},
    doi={10.1016/j.ejc.2006.11.002},
    archivePrefix={arXiv},
    eprint={cs/0601128},
    primaryClass={cs.CG}
}