Matroid minor

Matroid obtained by restrictions and contractions

In the mathematical theory of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations. Matroid minors are closely related to graph minors, and the restriction and contraction operations by which they are formed correspond to edge deletion and edge contraction operations in graphs. The theory of matroid minors leads to structural decompositions of matroids, and characterizations of matroid families by forbidden minors, analogous to the corresponding theory in graphs.

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