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Abstract
Let A(n,m) be a graph chosen uniformly at random from the class of all vertexlabelled 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 2core. 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, LeibnizZentrum fü Informatik GmbH 
Number of pages  16 
ISBN (Electronic)  9783959771474 
ISBN (Print)  18688969 
DOIs  
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
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 1 Active

Doctoral Program: Discrete Mathematics
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., SavaHuss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D. & Berkes, I.
1/05/10 → 31/12/22
Project: Research project