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Random trees and random graphs
Author(s) -
Łuczak Tomasz
Publication year - 1998
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(199810/12)13:3/4<485::aid-rsa16>3.0.co;2-y
Subject(s) - struct , random graph , combinatorics , mathematics , random regular graph , limit (mathematics) , random tree , discrete mathematics , graph , computer science , chordal graph , mathematical analysis , 1 planar graph , artificial intelligence , motion planning , robot , programming language
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