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.
Original languageEnglish
Title of host publication31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
EditorsMichael Drmota, Clemens Heuberger
Place of PublicationSaarbrücken/Wadern
PublisherSchloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH
Number of pages16
ISBN (Electronic)9783959771474
ISBN (Print)18688969
DOIs
Publication statusPublished - 2020
Event31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - https://www.math.aau.at/AofA2020/, Virtuell, Austria
Duration: 15 Jun 202019 Jun 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPICS
Volume159

Conference

Conference31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Abbreviated titleAofA2020
Country/TerritoryAustria
CityVirtuell
Period15/06/2019/06/20

Fields of Expertise

  • Information, Communication & Computing

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