Random Structures and Algorithms · 1998 · 50 citations · 0 references
Natural SciencesMathematicsCombinatoricsProbability TheoryStochastic ProcessesGraph TheoryLimit TheoremsNetwork DiameterProbabilistic CombinatoricsAsymptotic TheoryLimit LawsRandom Graph ModelsRandom Graph TheoryRandom GraphsRandom TreesTree Diameter
In the paper we study the asymptotic behavior of the number of trees with n vertices and diameter k=k(n), where (n−k)/n→a as n→∞ for some constant a<1. We use this result to determine the limit distribution of the diameter of the random graph G(n, p) in the subcritical phase. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 485–500, 1998