Random Planar Maps and Graphs with Minimum Degree Two and Three

  • Marc Noy Universitat Polit├Ęcnica de Catalunya Barcelona Graduate School of Mathematics
  • Lander Ramos
Keywords: Asymptotic enumeration, Planar graphs, Random graphs

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.

Published
2018-10-05
Article Number
P4.5