License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2020.18
URN: urn:nbn:de:0030-drops-120488
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12048/
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Kang, Mihyun ; Missethan, Michael

The Giant Component and 2-Core in Sparse Random Outerplanar Graphs

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Abstract

Let A(n,m) be a graph chosen uniformly at random from the class of all vertex-labelled outerplanar graphs with n vertices and m edges. We consider A(n,m) in the sparse regime when m=n/2+s for s=o(n). We show that with high probability the giant component in A(n,m) emerges at m=n/2+O (n^{2/3}) and determine the typical order of the 2-core. In addition, we prove that if s=ω(n^{2/3}), with high probability every edge in A(n,m) belongs to at most one cycle.

BibTeX - Entry

@InProceedings{kang_et_al:LIPIcs:2020:12048,
  author =	{Mihyun Kang and Michael Missethan},
  title =	{{The Giant Component and 2-Core in Sparse Random Outerplanar Graphs}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{18:1--18:16},
  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/2020/12048},
  URN =		{urn:nbn:de:0030-drops-120488},
  doi =		{10.4230/LIPIcs.AofA.2020.18},
  annote =	{Keywords: giant component, core, outerplanar graphs, singularity analysis}
}

Keywords: giant component, core, outerplanar graphs, singularity analysis
Collection: 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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