Three cottage problem
The
three cottage problem is a problem in
mathematical graph theory:
- Suppose there are three cottages that each need to be connected to the gas, water, and electric companies. Is there a way to do so without any of the lines crossing each other?
In more formal terms, this asks whether the
bipartite graph K
3,3 is
planar.
Kazimierz Kuratowski proved in 1930 that K
3,3 is nonplanar, and thus that the three cottage problem has no solution.