Depending on the definition of "touches," such map would contradict the four-color theorem.
I started doing a Topology problem for fun, now I can't even solve it and its driving me CRAZY!!!! A father is dying and he wants to leave his land to his five sons. The sons want to divide the land up so that each plot of land touches every other plot of land. That picture shows what they thought would work, but then they realized it didn't so they tried to make another map. What was the other map? I've tried to solve it many times, but I just can't figure it out! These are some of my failed results so that you don't make the mistake of trying them: PLEASE HELP!
Depending on the definition of "touches," such map would contradict the four-color theorem.
Have you heard of the four color theorem?
Edit: Oops, somehow I managed to miss that this was already mentioned.