Show that:
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1) if the radius-C-ball of each node has at least k nodes, then
the graph can be transformed into a graph with diameter at most 4C+2
by adding at most n/k edges.

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2) if the radius-C-ball of at least (1-1/k)n of the nodes contains at least
k nodes, then the graph can be transformed into a graph with diameter at
most 4C+2 by adding at most 2n/k edges