On longest paths and diameter in random apollonian networks

DOI10.1002/rsa.20538zbMath1314.05185arXiv1303.5213OpenAlexW1492951456MaRDI QIDQ5256390

Ehsan Ebrahimzadeh, Abbas Mehrabian, Jonathan Zung, Pu Gao, Linda Farczadi, Cristiane M. Sato, Nicholas C. Wormald

Publication date: 22 June 2015

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5213

zbMATH Keywords

random Apollonian networkslongest pathsheight of random treesdiameters of power-law graphsrandom plane graphs

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Planar graphs; geometric and topological aspects of graph theory (05C10) Distance in graphs (05C12)

Related Items (6)

SMALL-WORLD EFFECT IN GEOGRAPHICAL ATTACHMENT NETWORKS ⋮ Justifying the small-world phenomenon via random recursive trees ⋮ Heavy subtrees of Galton-Watson trees with an application to Apollonian networks ⋮ Some Properties of Random Apollonian Networks ⋮ Long Paths in Random Apollonian Networks ⋮ The height of random k‐trees and related branching processes

Cites Work

• Unnamed Item
• The random multisection problem, travelling waves and the distribution of the height of \(m\)-ary search trees
• Large deviations for the weighted height of an extended class of trees
• Some families of increasing planar maps
• Long cycles in 3-connected graphs
• On Certain Properties of Random Apollonian Networks
• High-dimensional Apollonian networks
• Random Trees

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