The longest minimum-weight path in a complete graph
Combinatorics
2009-02-06 v2 Probability
Abstract
We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables. We show that the longest of these minimum-weight paths has about \alpha^* \log nalpha log(alpha) - \alpha =1. This answers a question posed by Janson (1999).
Keywords
Cite
@article{arxiv.0809.0275,
title = {The longest minimum-weight path in a complete graph},
author = {Louigi Addario-Berry and Nicolas Broutin and Gabor Lugosi},
journal= {arXiv preprint arXiv:0809.0275},
year = {2009}
}
Comments
21 pages; minor corrections and clarifications