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Graphic Splitting of Cographic Matroids

Naiyer Pirouz (2015)

Discussiones Mathematicae Graph Theory

In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.

Graphs for n-circular matroids

Renata Kawa (2010)

Discussiones Mathematicae Graph Theory

We give "if and only if" characterization of graphs with the following property: given n ≥ 3, edges of such graphs form matroids with circuits from the collection of all graphs with n fundamental cycles. In this way we refer to the notion of matroidal family defined by Simões-Pereira [2].

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