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.
@article{10_37236_7640,
author = {Marc Noy and Lander Ramos},
title = {Random planar maps and graphs with minimum degree two and three},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/7640},
zbl = {1398.05112},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7640/}
}
TY - JOUR
AU - Marc Noy
AU - Lander Ramos
TI - Random planar maps and graphs with minimum degree two and three
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/7640/
DO - 10.37236/7640
ID - 10_37236_7640
ER -
%0 Journal Article
%A Marc Noy
%A Lander Ramos
%T Random planar maps and graphs with minimum degree two and three
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7640/
%R 10.37236/7640
%F 10_37236_7640
Marc Noy; Lander Ramos. Random planar maps and graphs with minimum degree two and three. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7640
