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arXiv · 1403.5211

Random planar maps and graphs with minimum degree two and three

Marc Noy·Lander Ramos
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Abstract

We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to the core of a random planar graph is of order c log(n) for an explicit constant c. These results provide new information on the structure of random planar graphs.

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Marc Noy, Lander Ramos. 2018-06-10. Random planar maps and graphs with minimum degree two and three. https://arxiv.org/abs/1403.5211

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