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

M. Kang; M. Missethan

doi:10.4230/LIPIcs.AofA.2020.18

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

M. Kang, M. Missethan

Institute of Discrete Mathematics (5050)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

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 language	English
Title of host publication	31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Editors	Michael Drmota, Clemens Heuberger
Place of Publication	Saarbrücken/Wadern
Publisher	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages	16
ISBN (Electronic)	9783959771474
ISBN (Print)	18688969
DOIs	https://doi.org/10.4230/LIPIcs.AofA.2020.18
Publication status	Published - 2020
Event	31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - https://www.math.aau.at/AofA2020/, Virtuell, Austria Duration: 15 Jun 2020 → 19 Jun 2020

Publication series

Name	Leibniz International Proceedings in Informatics, LIPICS
Volume	159

Conference

Conference	31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Abbreviated title	AofA2020
Country/Territory	Austria
City	Virtuell
Period	15/06/20 → 19/06/20

Fields of Expertise

Information, Communication & Computing

Access to Document

10.4230/LIPIcs.AofA.2020.18Licence: CC BY 4.0

Cite this

Kang, M., & Missethan, M. (2020). The Giant Component and 2-Core in Sparse Random Outerplanar Graphs. In M. Drmota, & C. Heuberger (Eds.), 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms Article 18 (Leibniz International Proceedings in Informatics, LIPICS; Vol. 159). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.AofA.2020.18

The Giant Component and 2-Core in Sparse Random Outerplanar Graphs. / Kang, M.; Missethan, M.
31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. ed. / Michael Drmota; Clemens Heuberger. Saarbrücken/Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. 18 (Leibniz International Proceedings in Informatics, LIPICS; Vol. 159).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Kang, M & Missethan, M 2020, The Giant Component and 2-Core in Sparse Random Outerplanar Graphs. in M Drmota & C Heuberger (eds), 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms., 18, Leibniz International Proceedings in Informatics, LIPICS, vol. 159, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Saarbrücken/Wadern, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms , Virtuell, Austria, 15/06/20. https://doi.org/10.4230/LIPIcs.AofA.2020.18

Kang M, Missethan M. The Giant Component and 2-Core in Sparse Random Outerplanar Graphs. In Drmota M, Heuberger C, editors, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. Saarbrücken/Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. 2020. 18. (Leibniz International Proceedings in Informatics, LIPICS). doi: 10.4230/LIPIcs.AofA.2020.18

Kang, M. ; Missethan, M. / The Giant Component and 2-Core in Sparse Random Outerplanar Graphs. 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. editor / Michael Drmota ; Clemens Heuberger. Saarbrücken/Wadern : Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. (Leibniz International Proceedings in Informatics, LIPICS).

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

Abstract

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Doctoral Program: Discrete Mathematics

Cite this

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

Abstract

Publication series

Conference

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Projects

Doctoral Program: Discrete Mathematics

Cite this