00:01
So this problem is an application of the degree sum formula.
00:06
So just to recall, the degree sum formula says that if you sum the degree of each vertex over all the vertices in the graph, this is equal to two times the number of edges, the total number of edges in the graph.
00:25
So how are we going to use this? well, so we're going to prove this by contradiction.
00:32
We're going to prove the statement you have by contradiction.
00:34
So suppose this means that suppose that every vertex has degree at least two.
00:54
Because if it didn't have at least two, then there would be a vertex of degree one or degree zero, and the statement would be proved.
01:03
So if it didn't have a degree of one or degree zero, then that means that every vertex has a degree at least two.
01:12
So then let's use the formula.
01:13
So, okay, let's actually first, let's write this in more mathematical terms.
01:20
So what does this mean? this means that degree of v has to be bigger than or equal to 2...