How to determine if a random graph with a fixed degree sequence has a giant component
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 de...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/133718 |
| Acesso em linha: | https://hdl.handle.net/2117/133718 https://dx.doi.org/10.1007/s00440-017-0757-1 |
| Access Level: | acceso abierto |
| Palavra-chave: | Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | 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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