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Graphoid


A graphoid consists of a set M of elements together with two collections C and D of nonempty subsets of M, called circuits and cocircuits respectively, such that

1. For any C in C and D in D, |C intersection D|!=1,

2. No circuit properly contains another circuit and no cocircuit properly contains another cocircuit,

3. For any painting of M with colors exactly one element green and the rest either red or blue, there exists either (a) a circuit C containing the green element and no red elements, or (b) a cocircuit D containing the green element and no blue elements.


See also

Matroid

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References

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

Referenced on Wolfram|Alpha

Graphoid

Cite this as:

Weisstein, Eric W. "Graphoid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Graphoid.html

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