# On the diameter of random planar graphs

Abstract : We show that the diameter $D(G_n)$ of a random (unembedded) 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 $P(D(G_n) \in (n^{1/4-\epsilon} ,n^{1/4+\epsilon})) \geq 1-\exp (-n^{c\epsilon})$ for $\epsilon$ small enough and $n$ large enough $(n \geq n_0(\epsilon))$. We prove similar statements for rooted $2$-connected and $3$-connected embedded (maps) and unembedded planar graphs.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [19 references]

https://hal.inria.fr/hal-00714713
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 4:33:24 PM
Last modification on : Friday, December 18, 2020 - 5:12:01 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:10:18 AM

### File

dmAM0105.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-00714713, version 2

### Citation

Guillaume Chapuy, Eric Fusy, Omer Gimenez, Marc Noy. On the diameter of random planar graphs. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.65-78. ⟨hal-00714713v2⟩

Record views