Random graphs

By Svante Janson, T. Luczak, Andrzej Rucinski. Wiley-Interscience series in discrete mathematics and optimization, 2000

1,480 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0612d96b8fcdd6a9c6da44cb56931951aef5fd02

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Citations in the corpus

Moment inequalities for functions of independent random variables (2005, background): “her order, naive applications of Theorem 15 may not lead to optimal results. Moment growth may actually depend on the special structure of T . Consider the prototypical triangle counting problem (see [18] for a general introduction to the subgraph counting problem). In the G(n,p) model, a random gra”
Novel scaling limits for critical inhomogeneous random graphs (2009, neutral): “m graphs has received tremendous attention in the past decades. The simplest example of a random graph is the Erd˝os–R´enyi random graph, whose critical regime has been intensely explored (see, e.g., [2, 5, 10, 19, 26] and the references therein). In the past few years, many examples of real-world n”
Mathematical results on scale‐free random graphs (2005, background): “Many of the results are presented in the monographs [11] and [38].”
Asymptotic normality of the k-core in random graphs (2006, methodology): “r(n)) −→d X∞ r=0 (8.9) ar(p)Ur. Indeed, by the joint convergence in (P8.5), this holds for the partial sums R r=0 for any ﬁnite R. Moreover, it follows easily from the exact formula for Varur(n) (see [18], Example 6.35) that, for any given Msuch that supn λn ≤ M, n−1Varu (8.10) r(n)= O(Mr/r!) unifor”
Concentration Inequalities and Martingale Inequalities: A Survey (2006, background): “The reader is referred to numerous textbooks [5, 17, 20] on this subject.”
Subnetwork hierarchies of biochemical pathways (2002, methodology): “tering trees of the other 43 organisms of the WIT database (Overbeek et al., 2000) used in this study can be seen on http://www.tp.umu.se/forskning/networks/meta/. the total number of nodes, see e.g. Janson et al., 2000). Close to the root (i.e. in the top of Fig. 3) the giant componentisstillexiste”
Poisson convergence in the restricted k-partitioning problem (2007, methodology): “The diameter and connectivity of random graphs has been well-studied, see for example the books of Bollobás [6] and Janson, Luczak, and Ruciński [20].”
Poisson Cloning Model for Random Graphs (2008, methodology): “13 in [44].”
A de Finetti representation for finite symmetric quantum states (2004, background): “n diﬀerence is that Lemma 4.2 is replaced by a statement based on a tail inequality due to Hoeﬀding [Hoe63] which applies to hypergeometric distributions as deﬁned below (for more details, see, e.g., [JLR00]). Deﬁnition A.2. The hypergeometricdistribution with parameters n, m, and k, denoted Hyp(n,m”