A Frankl-complete configuration is a finite family 
of sets with support 
, the set of elements
occurring in its members, such that every finite union-closed
set 
containing 
has an element of 
belonging to at least half the members of 
. Thus the configuration is a local certificate for the union-closed sets conjecture: whenever
it occurs within a larger union-closed set, one
of the elements already in its support must be frequent.
A configuration that is not Frankl-complete is called Non-FC. This does not make it a counterexample to the conjecture, since a
witnessing union-closed set may have a frequent
element outside 
. Morris (2006) studied Frankl-complete configurations under
the name FC-families.
