So I'm reading about k-connected graphs, and I'm a little confused about them. This is the main definition I've seen:
A graph is k connected if and only if for any distinct x, y vertices in the graph, there are k internally disjoint paths from x to y in the graph
This makes me think that a k-connected graph is also a k-1 connected graph, since if it's k-connected there must exist k internally disjoint paths (which implies there must exist k-1 internally disjoint paths which means it must also be k-1 connected). Is this true? Or am I missing something?