Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Drmota, Michael; Noy, Marc; Stufler, Benedikt https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-120403
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Cut Vertices in Random Planar Maps

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Abstract

The main goal of this paper is to determine the asymptotic behavior of the number X_n of cut-vertices in random planar maps with n edges. It is shown that X_n/n → c in probability (for some explicit c>0). For so-called subcritial subclasses of planar maps like outerplanar maps we obtain a central limit theorem, too.

BibTeX - Entry

@InProceedings{drmota_et_al:LIPIcs:2020:12040,
  author =	{Michael Drmota and Marc Noy and Benedikt Stufler},
  title =	{{Cut Vertices in Random Planar Maps}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Michael Drmota and Clemens Heuberger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12040},
  URN =		{urn:nbn:de:0030-drops-120403},
  doi =		{10.4230/LIPIcs.AofA.2020.10},
  annote =	{Keywords: random planar maps, cut vertices, generating functions, local graph limits}
}

Keywords: random planar maps, cut vertices, generating functions, local graph limits
Seminar: 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)
Issue date: 2020
Date of publication: 10.06.2020


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