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Graph limits of random unlabelled k-trees

Part of: Combinatorics Combinatorial probability Graph theory

Published online by Cambridge University Press:  18 May 2020

Emma Yu Jin  and
Benedikt Stufler
Emma Yu Jin
Affiliation:
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern Platz 1, 1090Vienna, Austria
Benedikt Stufler
Affiliation:
Institut für Mathematik, Universität München, Theresienstr. 39, D-80333Munich, Germany
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Abstract

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We study random unlabelled k-trees by combining the colouring approach by Gainer-Dewar and Gessel (2014) with the cycle-pointing method by Bodirsky, Fusy, Kang and Vigerske (2011). Our main applications are Gromov–Hausdorff–Prokhorov and Benjamini–Schramm limits that describe their asymptotic geometric shape on a global and local scale as the number of (k + 1)-cliques tends to infinity.

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs 05A16: Asymptotic enumeration
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 5 , September 2020 , pp. 722 - 746
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

†

The first author was supported by FWF-MOST (Austrian–Taiwanese) project I 2309-N35 and FWF Project P 32305.

‡

The second author gratefully acknowledges support by the German Research Foundation DFG, STU 679/1-1 and the Swiss National Science Foundation grant number 200020_172515.

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