Identify all combinations of sets which don't have intersection

Question

Let there are several (more than one) sets. And every set has at least one common element with other set. It is required to identify all possible versions of combination of sets which don't have a common element. Such combination must be "maximal" it means that this is impossible to add one more set to current combination without intersection with other sets.

For instance:
Example 1:
Let:

 1    
 |    
 2---4---5
 |
 3

$$A \{1, 2, 3\}$$ $$B \{2, 4, 5\}$$

Solution should be: $\{A\}, \{B\}.$

Example 2:

     6
     |
 1   7
 |   |
 2---4---5
 |
 3

$$A \{1, 2, 3\}$$ $$B \{2, 4, 5\}$$ $$C \{6, 7, 4\}$$

Solution should be: $\{A, C\}, \{B\}.$ But not: $\{A\}, \{B\}$ or $\{C\}, \{B\}$ - this is what means by "maximal".

I believe that this problem is been already known or can be represented in terms of other known problem.

So my question is: has this problem already is known?

Answer 1

If construct graph, when each vertex represents one set and edges connect only vertex which have intersection, then my problem can be represented as Listing all maximal independent sets and solved using the Bron-Kerbosch algorithm.