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

100%

Dalvi K., Borse Y., Shikare M.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 3

601-606

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).

Graphic Splitting of Cographic Matroids

88%

Pirouz N.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 1

95-104

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

88%

Dalvi K., Borse M., Shikare M.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 3

629-644

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.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

2 Dalvi K.

2 Shikare M.

1 Borse M.

1 Borse Y.

1 Pirouz N.

1 2015

1 2011

1 2009

Wyniki wyszukiwania

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

Graphic Splitting of Cographic Matroids

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