Noy, M., Requilé, C., & Rué, J. (2020). Further results on random cubic planar graphs. Random Structures and Algorithms, 56(3), 892–924. https://doi.org/10.1002/rsa.20893
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Journal:
Random Structures and Algorithms
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ISSN:
1042-9832
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Date (published):
2020
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Number of Pages:
33
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Publisher:
WILEY
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Peer reviewed:
Yes
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Keywords:
Applied Mathematics; Software; General Mathematics; Computer Graphics and Computer-Aided Design
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Abstract:
We provide precise asymptotic estimates for the number of several classes of labeled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by Bodirsky and coworkers. We revisit their work and obtain new results on the enumeration of cubic planar graphs and on random cubic planar graphs. In particular, we determine the exact probability of a random cubic planar graph being connected, and we show that the distribution of the number of triangles in random cubic planar graphs is asymptotically normal with linear expectation and variance. To the best of our knowledge, this is the first time one is able to determine the asymptotic distribution for the number of copies of a fixed graph containing a cycle in classes of random planar graphs arising from planar maps.
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Research Areas:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%