Two critical periods in the evolution of random planar graphs

DOI10.1090/S0002-9947-2012-05502-4zbMath1269.05027arXiv1006.0444OpenAlexW2057857650MaRDI QIDQ2841352

Tomasz Łuczak, Mihyun Kang

Publication date: 25 July 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.0444

zbMATH Keywords

embedded graphswell-labeled trees

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10) Asymptotic enumeration (05A16)

Related Items (15)

The Early Evolution of the Random Graph Process in Planar Graphs and Related Classes ⋮ Enumeration of cubic multigraphs on orientable surfaces ⋮ Concentration of maximum degree in random planar graphs ⋮ Random graphs from a weighted minor-closed class ⋮ Longest and shortest cycles in random planar graphs ⋮ The evolution of random graphs on surfaces ⋮ Evolution of the giant component in graphs on orientable surfaces ⋮ Random cubic planar graphs converge to the Brownian sphere ⋮ Cubic graphs and related triangulations on orientable surfaces ⋮ The Evolution of Random Graphs on Surfaces ⋮ Phase transitions in graphs on orientable surfaces ⋮ Critical random forests ⋮ On the probability of planarity of a random graph near the critical point ⋮ The Bohman-Frieze process near criticality ⋮ Spanning trees in random series-parallel graphs

Cites Work

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• Random graphs '85. Based on lectures presented at the 2nd International Seminar on Random Graphs and Probabilistic Methods in Combinatorics, Poznań, Poland, August 5-9, 1985, organized and sponsored by the Institute of Mathematics, Adam Mickiewicz University, Poznań, Poland
• Random graphs on surfaces
• Cycles in random graphs
• The number of rooted maps on an orientable surface
• On random planar graphs, the number of planar graphs and their triangulations
• Random planar lattices and integrated superBrownian excursion
• Random planar graphs
• Planar maps as labeled mobiles
• The number of labeled 2-connected planar graphs
• The evolution of uniform random planar graphs
• The topological structure of scaling limits of large planar maps
• Asymptotic enumeration and limit laws for graphs of fixed genus
• Random maps, coalescing saddles, singularity analysis, and Airy phenomena
• Asymptotic enumeration and limit laws of planar graphs
• A Census of Planar Triangulations
• Random cubic planar graphs
• On the Maximum Degree of a Random Planar Graph
• The Evolution of Random Graphs
• Component behavior near the critical point of the random graph process
• The Structure of a Random Graph at the Point of the Phase Transition
• Components of Random Forests
• The birth of the giant component
• The random planar graph process
• The phase transition in the cluster‐scaled model of a random graph
• A Census of Planar Maps

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