Subgraph counts for dense random graphs with specified degrees

Catherine Greenhill, Mikhail Isaev, Brendan D. McKay

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    1 Citation (Scopus)

    Abstract

    We prove two estimates for the expectation of the exponential of a complex function of a random permutation or subset. Using this theory, we find asymptotic expressions for the expected number of copies and induced copies of a given graph in a uniformly random graph with degree sequence(d 1 , ..., d n ) as n→ ∞. We also determine the expected number of spanning trees in this model. The range of degrees covered includes d j = λn + O(n 1/2+ϵ ) for some λ bounded away from 0 and 1.

    Original languageEnglish
    Pages (from-to)460-497
    Number of pages38
    JournalCombinatorics Probability and Computing
    Volume30
    Issue number3
    DOIs
    Publication statusPublished - 5 May 2021

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