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Generalized splitting operation for binary matroids and its applications. (English) Zbl 1247.05054

Summary: We introduce the notion of generalized splitting operation for binary matroids as an extension of the corresponding operation for graphs. The circuits and the bases of the new matroid are characterized. Under the reverse operation, we determine those binary matroids, each of which yields a given matroid by applying the splitting operation on them.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C83 Graph minors

Keywords:

circuit
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