How to determine if a random graph with a fixed degree sequence has a giant component

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/133718

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.contributor.author	Joos, Felix
dc.contributor.author	Perarnau Llobet, Guillem
dc.contributor.author	Rautenbach, Dieter
dc.contributor.author	Reed, Bruce
dc.date	2017-01-26
dc.identifier.citation	Joos, F. [et al.]. How to determine if a random graph with a fixed degree sequence has a giant component. "Probability theory and related fields", 26 Gener 2017, vol. 170, núm. 1-2, p. 263-310.
dc.identifier.citation	0178-8051
dc.identifier.citation	https://arxiv.org/abs/1601.03714
dc.identifier.citation	10.1007/s00440-017-0757-1
dc.identifier.uri	http://hdl.handle.net/2117/133718
dc.language.iso	eng
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject	Graph theory
dc.subject	Grafs, Teoria de
dc.title	How to determine if a random graph with a fixed degree sequence has a giant component
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	For a fixed degree sequence D=(d1,…,dn) , let G(D) be a uniformly chosen (simple) graph on {1,…,n} where the vertex i has degree di . In this paper we determine whether G(D) has a giant component with high probability, essentially imposing no conditions on D . We simply insist that the sum of the degrees in D which are not 2 is at least ¿(n) for some function ¿ going to infinity with n. This is a relatively minor technical condition, and when D does not satisfy it, both the probability that G(D) has a giant component and the probability that G(D) has no giant component are bounded away from 1

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