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Forbidden-minor characterization for the class of graphic element splitting matroids. (English) Zbl 1194.05017

Summary: This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids \(M\) have the property that the element splitting operation, by every pair of elements on \(M\) yields a graphic matroid. This problem is solved by proving that there is exactly one minor-minimal matroid that does not have this property.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
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