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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.
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 41, 1994.
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