I'm trying to understand Wikipedia's definition of "Degeneracy (graph theory)" which says:
In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges.
But then I look at the example and it does not make sense to me. Here is the graphic:
Now, from what I understand, a subgraph can be any subset of vertices and edges from the original graph. If so, one vertex can be a subgraph. If so, the 2-degenerate graph has many single vertices (aka subgraphs) that touch more than 2 edges.
I am sure I am missing something, but I don't know what it is.