On the diameter of random planar graphs
Abstract
We show that the diameter D(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1), in probability. More precisely there exists a constant c>0 such that the probability that D(Gn) lies in the interval (n1/4-ε,n1/4+ε) is greater than 1-(-ncε) for ε small enough and n>n0(ε). We prove similar statements for 2-connected and 3-connected planar graphs and maps.
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