TY - JOUR

T1 - Subgraph counts for dense random graphs with specified degrees

AU - Greenhill, Catherine

AU - Isaev, Mikhail

AU - McKay, Brendan D.

N1 - Publisher Copyright:
© 2020 The Author(s). Published by Cambridge University Press.

PY - 2021/5/5

Y1 - 2021/5/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85095790506&partnerID=8YFLogxK

U2 - 10.1017/S0963548320000498

DO - 10.1017/S0963548320000498

M3 - Article

SN - 0963-5483

VL - 30

SP - 460

EP - 497

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 3

ER -