00:01
We're given a graph and we're asked to determine if this graph is a pointer and if so to draw the graph so that no edges cross.
00:12
The graph we're given has six vertices, a, b, c, d, e, and f.
00:35
And you see if there's an edge from a to d and a to f is also the edge b -d, b -d, b -e, and the edges c -d, c -f.
01:10
And now with partition these vertices into two sets, so the one set of vertices m will contain a, b, and c, and the other set m, n, sorry, will contain the rest of the vertices, d, b, and f.
01:42
Now, notice that an element in m is connected only to elements in n and to no element in m.
01:52
And we also have that an element in n is connected only to elements in m and to no element in n.
02:02
So it follows that our graph is a subgraph of the complete bipartite graph k33.
02:19
However, the graph does not contain a subgraph that is homeomorphic to k3.
02:48
For example, we are missing the edge a .e, which would be necessary for k33.
02:57
And so the graph by theorem 2 is planar...