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Subgraphs of Dense Random Graphs with Specified Degrees

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dc.contributor.authorMcKay, Brendan
dc.date.accessioned2015-12-10T23:31:14Z
dc.date.issued2011
dc.date.updated2016-02-24T08:16:43Z
dc.description.abstractLet d = (d1, d2,dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph. Although there are many results of this kind, they are restricted to the sparse case with only a few exceptions. Our focus is instead on the case where the average degree is approximately a constant fraction of n. Our approach is the multidimensional saddle-point method. This extends the enumerative work of McKay and Wormald (1990) and is analogous to the theory developed for bipartite graphs by Greenhill and McKay (2009).
dc.identifier.issn0963-5483
dc.identifier.urihttp://hdl.handle.net/1885/68533
dc.publisherCambridge University Press
dc.sourceCombinatorics Probability and Computing
dc.subjectKeywords: Average degree; Bipartite graphs; Degree sequence; Greenhill; Induced subgraphs; Nonnegative integers; Random graphs; Saddlepoint method; Subgraphs; Graph theory
dc.titleSubgraphs of Dense Random Graphs with Specified Degrees
dc.typeJournal article
local.bibliographicCitation.lastpage433
local.bibliographicCitation.startpage413
local.contributor.affiliationMcKay, Brendan, College of Engineering and Computer Science, ANU
local.contributor.authoruidMcKay, Brendan, u8304521
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor080309 - Software Engineering
local.identifier.ariespublicationf2965xPUB1749
local.identifier.citationvolume20
local.identifier.doi10.1017/S0963548311000034
local.identifier.scopusID2-s2.0-80054932543
local.identifier.thomsonID000288758200006
local.type.statusPublished Version

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