# #18. On the Difficulty of Reducing the Diameter

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Prompts for discussion:

Some seemingly natural generalizations of the diameter-reduction goal:

Can we come up with a partition where most parts experience a reduction of diameter, for some suitable quantification of “most”?

Can we come up with a partition so that the diameter in each part reduces by at least a certain degree? For example, I figure that if we want the diameter in each part to be at most half of the original diameter, we would have to allow for many more parts. How many more?