3 Utilities | 3 Houses puzzle?
I am not sure if this question has been answered, and if that answer is part of Euclidean geometry (single plane/2 dimensional) or a part of Graph Theory.
If you have 3 nodes (A, B, C), is it impossible to draw an edge from each of these 3 nodes to 3 other nodes (1, 2, 3) without any of these edges intersecting?
+-----A-----+ | | | 1 2--C--3 | | | +-----B-----+
From the example above, you cannot draw an edge connecting C to 1, without intersecting one of the previous lines. (I would include a nice graphic, but my reputation won't let me)
- Has this been proven?
- If so, what is the name of this theorm?