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Title:
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Further results on random cubic planar graphs
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Author:
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Noy, M.; Requilé, C.; Rué, J.
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Abstract:
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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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Publication date:
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2019-10-13 |
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Subject (UDC):
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51 - Matemàtiques |
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Subject(s):
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Matemàtiques |
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Rights:
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L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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Pages:
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31 p. |
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Document type:
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Article
Article - Accepted version |
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DOI:
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10.1002/rsa.20893
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Published by:
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John Wiley and Sons Ltd
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Publish at:
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Random Structures and Algorithms
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Share:
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