English

Traveling in randomly embedded random graphs

Probability 2014-11-25 v1 Combinatorics

Abstract

We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a geodesic of length arbitrarily close to their Euclidean distance, and analyze the minimum length Traveling Salesperson Tour, extending the Beardwood-Halton-Hammersley theorem to this setting.

Keywords

Cite

@article{arxiv.1411.6596,
  title  = {Traveling in randomly embedded random graphs},
  author = {Alan Frieze and Wesley Pegden},
  journal= {arXiv preprint arXiv:1411.6596},
  year   = {2014}
}

Comments

25 pages, 2 figures

R2 v1 2026-06-22T07:10:27.974Z