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15,573
The diameter of sparse random graphs
 RANDOM STRUCTURES ALGORITHMS
, 2007
"... We derive an expression of the form c ln n+o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds asymptotically almost surely, assuming that certain convergence and supercriticality conditions are met, and is applicable to the classical random graph Gn ..."
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Cited by 11 (1 self)
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We derive an expression of the form c ln n+o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds asymptotically almost surely, assuming that certain convergence and supercriticality conditions are met, and is applicable to the classical random graph
The Diameter of Sparse Random Graphs
, 2004
"... Abstract We derive an expression of the form c ln n \Sigma o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds a.a.s., assuming certain convergence and supercriticality conditions are met. The proof is constructive and yields a method for computing th ..."
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Abstract We derive an expression of the form c ln n \Sigma o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds a.a.s., assuming certain convergence and supercriticality conditions are met. The proof is constructive and yields a method for computing
Bisecting Sparse Random Graphs
 Random Structures & Algorithms
, 2001
"... ABSTRACT: Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of ‘‘cross edges’ ’ between the parts. We are interested in sparse random graphs G with edge probability c�n. W ..."
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Cited by 4 (0 self)
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ABSTRACT: Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of ‘‘cross edges’ ’ between the parts. We are interested in sparse random graphs G with edge probability c
DISMANTLING SPARSE RANDOM GRAPHS
, 2007
"... We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph has no component with more than k vertices. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n → ∞, then the number in question is ..."
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Cited by 2 (0 self)
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We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph has no component with more than k vertices. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n → ∞, then the number in question
Sparse random graphs with clustering
, 2008
"... In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results about this extension. The basic idea is to construct the random ..."
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Cited by 9 (6 self)
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In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results about this extension. The basic idea is to construct the random
The diameter of sparse random graphs
 ADV. IN APPL. MATH
, 2001
"... We consider the diameter of a random graph G�n � p � for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of ..."
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Cited by 52 (1 self)
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We consider the diameter of a random graph G�n � p � for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter
The diameter of sparse random graphs
, 2010
"... In this paper we study the diameter of the random graph G(n,p), i.e., the largest finite distance between two vertices, for a wide range of functions p = p(n). For p = λ/n with λ> 1 constant we give a simple proof of an essentially best possible result, with an Op(1) additive correction term. Usi ..."
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Cited by 14 (0 self)
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In this paper we study the diameter of the random graph G(n,p), i.e., the largest finite distance between two vertices, for a wide range of functions p = p(n). For p = λ/n with λ> 1 constant we give a simple proof of an essentially best possible result, with an Op(1) additive correction term
On the Rigidity of Sparse Random Graphs
"... A graph with a trivial automorphism group is said to be rigid. Wright proved [11] that for lognn + ω( 1 n) ≤ p ≤ 12 a random graph G ∈ G(n, p) is rigid whp. It is not hard to see that this lower bound is sharp and for p < (1−) lognn with positive probability aut(G) is nontrivial. We show that in ..."
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A graph with a trivial automorphism group is said to be rigid. Wright proved [11] that for lognn + ω( 1 n) ≤ p ≤ 12 a random graph G ∈ G(n, p) is rigid whp. It is not hard to see that this lower bound is sharp and for p < (1−) lognn with positive probability aut(G) is nontrivial. We show
On the structure of the core of sparse random graphs
"... In this paper, we investigate the structure of the core of a sparse random graph above the critical point. We determine the asymptotic distributions of the total number of isolated cycles there as well as the joint distributions of the isolated cycles of fixed lengths. Furthermore, focusing on its ..."
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Cited by 1 (0 self)
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In this paper, we investigate the structure of the core of a sparse random graph above the critical point. We determine the asymptotic distributions of the total number of isolated cycles there as well as the joint distributions of the isolated cycles of fixed lengths. Furthermore, focusing
Flooding in weighted sparse random graphs
, 2013
"... In this paper, we study the impact of edge weights on distances in sparse random graphs. We interpret these weights as delays and take them as independent and identically distributed exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all ..."
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Cited by 6 (2 self)
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In this paper, we study the impact of edge weights on distances in sparse random graphs. We interpret these weights as delays and take them as independent and identically distributed exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all
Results 1  10
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15,573