Dynamic Erdős- Rényi random graph with forbidden degree
Résumé
As suggested by Itai Benjamini, we introduced a variant of the Erdős- Rényi random graph process with a forbidden degree $k$, in which every edge adjacent to a vertex $v$ is removed when the degree of $v$ reaches $k$ (but the removed edges may very well be added again later). We study the existence of a giant component, depending on the forbidden degree $k$ and the time parameter $t$. We prove that for $k>4$ a giant component appears at some point, while for $k<4$, a giant component never occurs. The main tool of our study is the local limit of the random graph process: it provides useful information about the cases $k>4$, but also the threshold case k=4.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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