2.9.4 k-Connectivity Video
PROFESSOR: So connectivity is more than just an all or nothing affair. We can talk about how connected a graph is. So let's begin with two vertices. Two vertices are said to be k-edge connected if they remain connected if you remove fewer than k edges from the graph. Let's look at an example. So here's a graph, and let's focus on those two vertices that I've highlighted in magenta. They are 1-edge connected because they're connected, and if you remove one edge they become disconnected. So they're 1-edge connected, but they're not 2-edge connected. In particular, if I delete that edge, then they no longer is a path between the two magenta vertices. Here's an example of two vertices, these two green vertices, that are 2-edge connected. That means that I can remove any number of edges less than two, which is to say one edge, and they'll stay connected. But if I do remove two vertices, they become disconnected. So with those two edges j...