The number of separating circles depends only on the two group sizes, and the cluster algebra of the higher-order Voronoi decomposition is independent of the dot configuration.
Algorithms in combinatorial geometry , volume 10 of EATCS Monographs on Theoretical Computer Science
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Separating dots with circles
The number of separating circles depends only on the two group sizes, and the cluster algebra of the higher-order Voronoi decomposition is independent of the dot configuration.