On the diameter of random planar graphs
Combinatorics
2019-02-20 v2
Abstract
We show that the diameter D(G_n) of a random labelled connected planar graph with n vertices is equal to n^{1/4+o(1)}, in probability. More precisely there exists a constant c>0 such that the probability that D(G_n) lies in the interval (n^{1/4-\epsilon},n^{1/4+\epsilon}) is greater than 1-\exp(-n^{c\epsilon}) for {\epsilon} small enough and n>n_0(\epsilon). We prove similar statements for 2-connected and 3-connected planar graphs and maps.
Keywords
Cite
@article{arxiv.1203.3079,
title = {On the diameter of random planar graphs},
author = {Guillaume Chapuy and Éric Fusy and Omer Giménez and Marc Noy},
journal= {arXiv preprint arXiv:1203.3079},
year = {2019}
}
Comments
24 pages, 7 figures