Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
A simple solution to the k-core problem
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
The k-core and branching processes
Combinatorics, Probability and Computing
A new approach to the giant component problem
Random Structures & Algorithms
The probability that a random multigraph is simple
Combinatorics, Probability and Computing
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We study the random graph Gn,λ-n conditioned on the event that all vertex degrees lie in some given subset $ {\cal S} $ of the nonnegative integers. Subject to a certain hypothesis on $ {\cal S} $, the empirical distribution of the vertex degrees is asymptotically Poisson with some parameter $ \hat{\mu} $ given as the root of a certain “characteristic equation” of $ {\cal S} $ that maximizes a certain function $ {\psi_{\cal S}(\mu)} $. Subject to a hypothesis on $ {\cal S} $, we obtain a partial description of the structure of such a random graph, including a condition for the existence (or not) of a giant component. The requisite hypothesis is in many cases benign, and applications are presented to a number of choices for the set $ {\cal S} $ including the sets of (respectively) even and odd numbers. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010