Suppose that is a pseudograph, is the edge set of , and is the family of edge sets of graph cycles of . Then obeys the axioms for the circuits of a matroid, and hence is a matroid. Any matroid that can be obtained in this way is a graphic matroid.

# Graphic Matroid

## See also

Matroid, Pseudograph
*This entry contributed by Dillon
Mayhew*

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## References

Oxley, J. G.*Matroid Theory.*Oxford, England: Oxford University Press, p. 11, 1991.

## Referenced on Wolfram|Alpha

Graphic Matroid## Cite this as:

Mayhew, Dillon. "Graphic Matroid." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/GraphicMatroid.html