Graphic matroid

Two different graphs (red) that are duals of the same planar graph (pale blue). Despite being non-isomorphic as graphs, they have isomorphic graphic matroids.

In matroid theory, a discipline within mathematics, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the forests in a given undirected graph. The dual matroids of graphic matroids are called co-graphic matroids or bond matroids. A matroid that is both graphic and co-graphic is called a planar matroid; these are exactly the graphic matroids formed from planar graphs.

单词	Graphic matroid
释义	Graphic matroid 英语百科 Graphic matroid In matroid theory, a discipline within mathematics, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the forests in a given undirected graph. The dual matroids of graphic matroids are called co-graphic matroids or bond matroids. A matroid that is both graphic and co-graphic is called a planar matroid; these are exactly the graphic matroids formed from planar graphs.
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