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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12048/
Kang, Mihyun ;
Missethan, Michael
The Giant Component and 2-Core in Sparse Random Outerplanar Graphs
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}
}
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Keywords: |
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giant component, core, outerplanar graphs, singularity analysis |
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Collection: |
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31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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10.06.2020 |
