The metric dimension of sparse random graphs
In 2013, Bollobás, Mitsche, and Pralat gave upper and lower bounds for the likely metric dimension of random Erdos-Rényi graphs G(n,p) for a large range of expected degrees. However, their results only apply when d=pn=omega(log^5 n), leaving open sparser random graphs with d=O(log^5 n) or d=o(log^5n...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::8f182b6969accb4ef065de9a8bd0aab4 |
| Acceso en línea: | https://hdl.handle.net/2117/461032 https://dx.doi.org/10.37236/14094 |
| Access Level: | acceso abierto |
| Palabra clave: | Sparse Random Graphs Random graphs Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | In 2013, Bollobás, Mitsche, and Pralat gave upper and lower bounds for the likely metric dimension of random Erdos-Rényi graphs G(n,p) for a large range of expected degrees. However, their results only apply when d=pn=omega(log^5 n), leaving open sparser random graphs with d=O(log^5 n) or d=o(log^5n). Here we provide upper and lower bounds on the likely metric dimension of G(n,p) in a range of d starting just above the connectivity transition, i.e., where d=c log n for some constant c>1, up to d=O(log^5 n). Our lower bound technique is based on an entropic argument which is weaker but more general than the use of Suen's inequality by Bollobás, Mitsche, and Pralat, whereas our upper bound is similar to theirs. |
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