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.
@InProceedings{kang_et_al:LIPIcs.AofA.2020.18, author = {Kang, Mihyun and Missethan, Michael}, 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 = {Drmota, Michael and Heuberger, Clemens}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.18}, URN = {urn:nbn:de:0030-drops-120488}, doi = {10.4230/LIPIcs.AofA.2020.18}, annote = {Keywords: giant component, core, outerplanar graphs, singularity analysis} }
Feedback for Dagstuhl Publishing