Reducing nearby enemies

You are given an irreflexive symmetric (but not necessarily transitive) “enemies” relation on a set of people.  In other words, if person A is an enemy of a person B, then B is also an enemy of A.  How can you divide up the people into two houses in such a way that every person has at least as many enemies in the other house as in their own house?

Hint:  Planar configuration of straight connecting lines puzzle may provide a hint to solving this puzzle.

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ronret45 Expert Asked on 1st August 2015 in Microsoft Interview Puzzles.
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