Graphic matroid

In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the forests in a given finite undirected graph. The dual matroids of graphic matroids are called co-graphic matroids or bond matroids.^[1] A matroid that is both graphic and co-graphic is sometimes called a planar matroid (but this should not be confused with matroids of rank 3, which generalize planar point configurations); these are exactly the graphic matroids formed from planar graphs.

^ Tutte (1965) uses a reversed terminology, in which he called bond matroids "graphic" and cycle matroids "co-graphic", but this has not been followed by later authors.

[1] Tutte (1965) uses a reversed terminology, in which he called bond matroids "graphic" and cycle matroids "co-graphic", but this has not been followed by later authors.

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