Graphoid

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.

REFERENCES

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