A graphoid consists of a set 
of elements together with two collections 
and 
of nonempty subsets of 
,
called circuits and cocircuits respectively, such that
1. For any 
and 
, 
,
2. No circuit properly contains another circuit and no cocircuit properly contains another cocircuit,
3. For any painting of 
with colors exactly one element green and the rest
either red or blue, there exists either (a) a circuit 
containing the green element and no red elements, or (b) a
cocircuit 
containing the green element and no blue elements.
