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

Institut für Diskrete Mathematik (5050)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

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.

Originalsprache	englisch
Titel	31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Redakteure/-innen	Michael Drmota, Clemens Heuberger
Erscheinungsort	Saarbrücken/Wadern
Herausgeber (Verlag)	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Seitenumfang	16
ISBN (elektronisch)	9783959771474
ISBN (Print)	18688969
DOIs	https://doi.org/10.4230/LIPIcs.AofA.2020.18
Publikationsstatus	Veröffentlicht - 2020
Veranstaltung	31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - https://www.math.aau.at/AofA2020/, Virtuell, Österreich Dauer: 15 Juni 2020 → 19 Juni 2020

Publikationsreihe

Name	Leibniz International Proceedings in Informatics, LIPICS
Band	159

Konferenz

Konferenz	31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Kurztitel	AofA2020
Land/Gebiet	Österreich
Ort	Virtuell
Zeitraum	15/06/20 → 19/06/20

Fields of Expertise

Information, Communication & Computing

Zugriff auf Dokument

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

Andere Dateien und Links

DK Diskrete Mathematik
Ebner, O., Lehner, F., Greinecker, F., Burkard, R., Wallner, J., Elsholtz, C., Woess, W., Raseta, M., Bazarova, A., Krenn, D., Lehner, F., Kang, M., Tichy, R., Sava-Huss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D., Berkes, I. & Kerber, M.
1/05/10 → 30/06/24
Projekt: Forschungsprojekt

Dieses zitieren

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

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

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

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title = "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.",

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

Abstract

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Projekte

DK Diskrete Mathematik

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