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• W1492951456 abstract "We consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face. After n – 3 steps, we obtain a random triangulated plane graph with n vertices, which is called a Random Apollonian Network (RAN). We show that asymptotically almost surely (a.a.s.) a longest path in a RAN has length o(n), refuting a conjecture of Frieze and Tsourakakis. We also show that a RAN always has a cycle (and thus a path) of length , and that the expected length of its longest cycles (and paths) is . Finally, we prove that a.a.s. the diameter of a RAN is asymptotic to , where is the solution of an explicit equation. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 703–725, 2014" @default.
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• W1492951456 date "2014-12-01" @default.
• W1492951456 modified "2023-09-24" @default.
• W1492951456 title "On longest paths and diameter in random apollonian networks" @default.
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• W1492951456 doi "https://doi.org/10.1002/rsa.20538" @default.
• W1492951456 hasPublicationYear "2014" @default.
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