Random planar maps and graphs with minimum degree two and three

2014/03/20 by Marc Noy, Noy, Marc, Lander Ramos +1
Computer Science · Mathematics · #05A16 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1403.5211

openalex publication_date 2014/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Degree distribution in random planar graphs
• Uniform Random Planar Graphs with Degree Constraints
• Further results on random cubic planar graphs
• The early evolution of the random graph process in planar graphs and related classes
• Radius and profile of random planar maps with faces of arbitrary degrees