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| HAL : hal-00714713, version 1 |
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| 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), Vienne : Autriche (2010) |
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| On the diameter of random planar graphs |
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| Guillaume Chapuy 1Eric Fusy 2 |
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| (01/09/2010) |
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| 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 ) ∈ (n^{1/4−e} , n^{1/4+e} )) ≥ 1 − exp(−nc(e) ) for e small enough and n large enough (n ≥ n0 (e)). We prove similar statements for rooted 2-connected and 3-connected embedded (maps) and unembedded planar graphs. |
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| 1 : | Department of Mathematics |
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Simon Fraser University |
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| 2 : | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| 3 : | Universitat Politècnica de Catalunya (UPC) |
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Universitat Politécnica de Catalunya |
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| Domaine | : | Mathématiques/Combinatoire |
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| planar graphs – diameter – asymptotics |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00714713, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00714713 | |
| oai:hal.archives-ouvertes.fr:hal-00714713 | |
| Contributeur : Eric Fusy | |
| Soumis le : Jeudi 5 Juillet 2012, 14:19:07 | |
| Dernière modification le : Jeudi 5 Juillet 2012, 14:34:24 | |
