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

Kiran Dalvi; Y.M. Borse; M.M. Shikare

Displaying similar documents to “Forbidden-minor characterization for the class of cographic element splitting matroids”

Graphic Splitting of Cographic Matroids

Naiyer Pirouz (2015)

Discussiones Mathematicae Graph Theory

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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.

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. ...