00:01
Hi, in this video we assume we have a finite graph g, and furthermore we assume that g has only two vertices with odd degree, so let's call them uv, and these are the only ones that have odd degree.
00:22
So what we're going to do here is we're going to prove that g contains a uv path.
00:28
So first, i don't know why this pen is being weird, so first of all, we'll do case 1, which is the that g is connected.
00:48
So in this case, if g is connected, then there exists a path between any two vertices.
01:11
So then it is of course true that there would be a path between you and v.
01:16
So the first case is trivial.
01:19
The second case is if g is not connected, and what we do is we let j be the connected component that contains the vertex u.
01:44
So g is going to consist of some connected components, and we let j be the one that contains you...