00:01
So our graph looks something like so, right? now, to have an euler trail or an euler path, we basically want to go over every edge exactly once.
00:10
We could go to a vertex more than once, we have to use every edge exactly once, and since this is a path, we can start and finish at a different vertex.
00:18
Now looking at the degree of the vertices, so the degree is basically how many edges are touching every vertex.
00:24
Well the degree of h is 2, the degree of i is 2, the degree of k is 2, degree of f is, well, 3, and l is 1, and j is actually 6.
00:34
So we have exactly two vertices of an odd degree, therefore this should have an euler trail or an euler path.
00:40
So let's say we start at the vertex of j.
00:46
Now can we do a path? if we go up, let's say you use the yellow edge here and go up to h, so j to h, and then that would use this edge, maybe we'll put a line through it.
00:57
Okay, now we could go down to f, that's going to use this edge, put a line through it.
01:05
We could go back to j, that's going to use this edge, and then, well we don't want to go to l yet, because if we go to l we're going to be stranded at l.
01:21
So we could, if we're at j right now, we could go, we can't go up to h, that would use the same edges, we could go over to g using the red edge.
01:33
So we could go over to g.
01:34
Okay, now we're at g, well we could go down to k, that would use this edge, so go down to k...