Asymptotic enumeration of graphs with given degree sequence

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We survey results on counting graphs with given degree sequence, focusing on asymptotic results, and mentioning some of the applications of these results. The main recent development is the proof of a conjecture that facilitates access to the degree sequence of a random graph via a model incorporating independent binomial random variables. The basic method used in the proof was to examine the changes in the counting function when the degrees are perturbed. We compare with several previous uses of this type of method.

Original languageEnglish
Title of host publicationProceedings of the International Congress of Mathematicians, ICM 2018
Subtitle of host publication2018 International Congress of Mathematicians, ICM 2018; Rio de Janeiro; Brazil; 1 August 2018 through 9 August 2018
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
Place of PublicationSingapore
PublisherWorld Scientific Publishing
Number of pages22
ISBN (Electronic)9789813272934
Publication statusPublished - 1 Jan 2018
EventInternational Congress of Mathematicians 2018 - Barra da Tijuca, Rio de Janeiro, Brazil
Duration: 1 Aug 20189 Aug 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018


ConferenceInternational Congress of Mathematicians 2018
Abbreviated titleICM 2018
CityRio de Janeiro
Internet address

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