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On the Diameter of Random Planar Graphs

  • GUILLAUME CHAPUY (a1), ÉRIC FUSY (a2), OMER GIMÉNEZ (a3) and MARC NOY (a4)

Abstract

We show that the diameter diam(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

$$ P(\D(G_n)\in(n^{1/4-\e},n^{1/4+\e}))\geq 1-\exp(-n^{c\e}) $$
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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Keywords

On the Diameter of Random Planar Graphs

  • GUILLAUME CHAPUY (a1), ÉRIC FUSY (a2), OMER GIMÉNEZ (a3) and MARC NOY (a4)

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