The distribution of the maximum vertex degree in random planar maps

DOI10.1006/jcta.1999.3006zbMath0944.05057OpenAlexW2087428017MaRDI QIDQ1971616

Nicholas C. Wormald, Zhi-Cheng Gao

Publication date: 24 September 2000

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f4275cde18e7770495154b664cd9ec392e159b65

zbMATH Keywords

probabilityvariancerandom variableexpectationrooted triangulationsrandom rooted map

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (20)

First-passage percolation in random planar maps and Tutte's bijection ⋮ Maximum degree in minor-closed classes of graphs ⋮ Part Sizes of Smooth Supercritical Compositional Structures ⋮ The CRT is the scaling limit of random dissections ⋮ Random non-crossing plane configurations: A conditioned Galton-Watson tree approach ⋮ The maximum degree of random planar graphs ⋮ A Markov Chain Sampler for Plane Curves ⋮ The shape of random pattern-avoiding permutations ⋮ The evolution of random graphs on surfaces ⋮ Simply Generated Non-Crossing Partitions ⋮ The Evolution of Random Graphs on Surfaces ⋮ On the Maximum Degree of a Random Planar Graph ⋮ Random stable laminations of the disk ⋮ On properties of random dissections and triangulations ⋮ Extremal statistics on non-crossing configurations ⋮ 4-edge-connected 4-regular maps on the projective plane ⋮ Random planar maps and graphs with minimum degree two and three ⋮ The Maximum Degree of Series-Parallel Graphs ⋮ The maximal degree in a Poisson-Delaunay graph ⋮ Distributions of near-4-regular maps on the sphere and the projective plane

Cites Work

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• The asymptotic number of rooted maps on a surface
• Properties of random triangulations and trees
• Root vertex valency distributions of rooted maps and rooted triangulations
• Almost all maps are asymmetric
• Singularity Analysis of Generating Functions
• The Size of the Largest Components in Random Planar Maps
• The Enumeration of Maps on the Torus and the Projective Plane
• Enumeration of Triangulations of the Disk

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