On the diameter of random planar graphs

Details On the diameter of random planar graphs On the diameter of random planar graphs

2012-03-14

arxiv.org/abs/1203.3079v1

Mathematics

Combinatorics

24 pages, 7 figures

Scientific paper

We show that the diameter D(G_n) of a random labelled connected planar graph with n vertices is asymptotically almost surely of order n^{1/4}, in the sense that 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.

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