10.1184/R1/6480137.v1 Alan Frieze Alan Frieze Wesley Pegden Wesley Pegden Traveling in randomly embedded random graphs Carnegie Mellon University 2014 Mathematical Sciences 2014-11-24 00:00:00 Journal contribution https://kilthub.cmu.edu/articles/journal_contribution/Traveling_in_randomly_embedded_random_graphs/6480137 <p>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.</p>