Random planar maps and graphs with minimum degree two and three [article]

Marc Noy, Lander Ramos
2018 arXiv   pre-print
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.
arXiv:1403.5211v2 fatcat:ymuyxrzpgrbn5k5n2fszgfsvau