On the Diameter of Random Planar Graphs

Author:

CHAPUY GUILLAUME,FUSY ÉRIC,GIMÉNEZ OMER,NOY MARC

Abstract

We show that the diameter diam(Gn) of a random labelled connected planar graph withnvertices is equal ton1/4+o(1), in probability. More precisely, there exists a constantc> 0 such that$$ P(\D(G_n)\in(n^{1/4-\e},n^{1/4+\e}))\geq 1-\exp(-n^{c\e}) $$for ε small enough andn ≥ n0(ε). We prove similar statements for 2-connected and 3-connected planar graphs and maps.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

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