Random graphs with forbidden vertex degrees
| dc.creator | Grimmett, Geoffrey | |
| dc.creator | Janson, Svante | |
| dc.date | 2007-12-03 | |
| dc.date.accessioned | 2026-07-07T08:46:54Z | |
| dc.date.available | 2026-07-07T08:46:54Z | |
| dc.description | We study the random graph G_{n,λ/n} conditioned on the event that all vertex degrees lie in some given subset S of the non-negative integers. Subject to a certain hypothesis on S, the empirical distribution of the vertex degrees is asymptotically Poisson with some parameter \mux given as the root of a certain `characteristic equation' of S that maximises a certain function \psis(μ). Subject to a hypothesis on S, we obtain a partial description of the structure of such a random graph, including a condition for the existence (or not) of a giant component. The requisite hypothesis is in many cases benign, and applications are presented to a number of choices for the set S including the sets of (respectively) even and odd numbers. The random \emph{even} graph is related to the random-cluster model on the complete graph K_n. | |
| dc.identifier | https://arxiv.org/abs/0712.0270 | |
| dc.identifier | http://arxiv.org/abs/0712.0270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143411 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 05C80, 05C07 | |
| dc.title | Random graphs with forbidden vertex degrees | |
| dc.type | text |