Graphic Splitting of Cographic Matroids

Naiyer Pirouz

Displaying similar documents to “Graphic Splitting of Cographic Matroids”

Forbidden-minor characterization for the class of cographic element splitting matroids

Kiran Dalvi, Y.M. Borse, M.M. Shikare (2011)

Discussiones Mathematicae Graph Theory

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In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K₄).

Forbidden-minor characterization for the class of graphic element splitting matroids

Kiran Dalvi, Y.M. Borse, M.M. Shikare (2009)

Discussiones Mathematicae Graph Theory

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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. ...