Aggregate elements of sets

I actually have a map of the form map>. Each key is an integer value and the value is a set with the elements that the key value can be aggregated with.

For example:

0: 0 1 3 4 6 7 9

1: 0 1 2 4 6

2: 1 2 4

3: 0 3 4 7 9

4: 0 1 2 3 4 6 7 9

5: 5 6 7 8

6: 0 1 4 5 6 7 8 9

7: 0 3 4 5 6 7 8 9

8: 5 6 7 8

9: 0 3 4 6 7 9

So, a possible aggregation, for K <= 4, where K represents the number of aggregated groups is:

k1: 0, 5, 7, 8

k2: 1, 2, 4, 6

k3: 3, 9

Another one:

k1: 0 3 4 7 9

k2: 5 6 8

k3: 1 2

If K <= 8, we can have the same aggregations but also:

k1: 0

k2: 1

k3: 2

k4: 3

k5: 4

k6: 5

k7: 6

k8: 7 8 9

Note that, in order to aggregate elements, these elements must be also possible to aggregate between them. For example:

We cannot aggregate: 0,1,3,4, because 3 cannot be aggregated with 1 (3: 0 3 4 7 9).

The problem is to find a possible aggregation, closer to K.

I tried pairing the elements, this is easy, but with this approach I can only get #elements/2 groups.

I would like to select the possible aggregation closer to K.