Largest component of subcritical random graphs with given degree sequence
We study the size of the largest component of two models of random graphs with prescribed degree sequence, the configuration model (CM) and the uniform model (UM), in the (barely) subcritical regime. For the CM, we give upper bounds that are asymptotically tight for certain degree sequences. These b...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/406424 |
| Acceso en línea: | https://hdl.handle.net/2117/406424 https://dx.doi.org/10.1214/23-EJP921 |
| Access Level: | acceso abierto |
| Palabra clave: | Discrete mathematics Graph theory Component structure Configuration model Largest component Local limit theorems Random graph with given degree sequence Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta |
| Sumario: | We study the size of the largest component of two models of random graphs with prescribed degree sequence, the configuration model (CM) and the uniform model (UM), in the (barely) subcritical regime. For the CM, we give upper bounds that are asymptotically tight for certain degree sequences. These bounds hold under mild conditions on the sequence and improve previous results of Hatami and Molloy on the barely subcritical regime. For the UM, we give weaker upper bounds that are tight up to logarithmic terms but require no assumptions on the degree sequence. In particular, the latter result applies to degree sequences with infinite variance in the subcritical regime. |
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