A k-core of a graph is the maximal subgraph with minimal degree k. For example, the 2-core would emerge by subsequently deleting degree-1 vertices of a graph.
I've seen a lot of work on existence of nontrivial k-cores of a random graph, and some on the number of vertices/edges in the k-core of a random graph. I would like to know if, for specific graph models, there are known theorems describing the distribution of the k-core, e.g. when the original graph is
Erdös Renyi or Configuration model/given degree sequence
will the resulting 2-core be distributed as ER/configuration?
A quick comment on previous works: Janson/Luczak published "Asymptotic normality of the k-Core in random graphs" as well as "A simple solution to the k-core problem". Cooper/Frieze/Lubetzky in their paper "Cover time of a random graph with a degree sequence II: Allowing vertices of degree two" calculated the distribution of the kernel in a configuration model with minimum degree 2, but I don't think their method works for the 2-core.
