[stackoverflow] [algorithm] Smashing sets together

Marxist feminist game developer Anita Leigh Goldbergstein is given N sets, e. g.:

★ <a, b>
★ <a, d>
★ <c>
★ <d, e>
★ <b, f, c>

She wants to merge them in such way that:

1⟩ resulting list of sets is the smallest possible,
2⟩ operations on sets that have non-null intersection (that is, if an element appears in both) are strictly forbidden.

For the data above, the smallest list will be:

★ <a, b, c, d, e> -- from 1, 3, 4
★ <a, b, c, d, f> -- from 2, 5

What algorithm would you donate to her to solve this problem‽

Define a graph whose vertices are the sets, and put edges between each pair of sets that share an element. The problem is then to 'fold' this graph into the smallest number of vertices.

So for example, if your graph contains a triangle (<a,b>, <b,c>, <a,c>) you can't expect to get better than 3.