Determination of the bases of a splitting matroid

Shikare, M. M.; Azadi, Ghodratollah

doi:10.1016/s0195-6698(02)00135-x

Cited by 17 publications

(7 citation statements)

References 4 publications

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“…The splitting operation, in general, does not preserve the connectedness of the binary matroid. Several results concerning splitting operation have been explored in [1,3,6,7].…”

Section: An Even Number Of Elements Of X}; Andmentioning

confidence: 99%

A characterization of n-connected splitting matroids

Malavadkar

Shikare

Dhotre

2014

Asian-European J. Math.

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“…The splitting operation, in general, does not preserve the connectedness of the binary matroid. Several results concerning splitting operation have been explored in [1,3,6,7].…”

Section: An Even Number Of Elements Of X}; Andmentioning

confidence: 99%

A characterization of n-connected splitting matroids

Malavadkar

Shikare

Dhotre

2014

Asian-European J. Math.

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“…Therefore by (5), (6) and (7) we have r(M * ) + 1 = r(M * ), a contradiction. This completes the proof.…”

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confidence: 90%

On dual of the generalized splitting matroids

Ghafari

Azadi

Azanchiler

2018

asat

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Given a binary matroid M and a subset T ⊆ E(M ), Luis A. Goddyn posed a problem that the dual of the splitting of M , i.e., ((MT ) * ) is not always equal to the splitting of the dual of M , ((M * )T ). This persuade us to ask if we can characterize those binary matroids for which (MT ) * = (M * )T . Santosh B. Dhotre answered this question for a two-element subset T . In this paper, we generalize his result for any subset T ⊆ E(M ) and exhibit a criterion for a binary matroid M and subsets T for which (MT ) * and (M * )T are the equal. We also show that there is no subset T ⊆ E(M ) for which, the dual of element splitting of M , i.e., ((M ′ T ) * ) equals to the element splitting of the dual of M , ((M * ) ′ T ).

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“…Shikare, Azadi and Waphare [6,7] extended the notions of n-point splitting from graphs to binary matroids. As the authors in [4] determinated the bases of splitting inatroids and Shikare, Azanchiler and Waphare [8] characterized cocircuits of splitting matroids. We extend the n-line splitting from graphs to binary matroids in next Section.…”

Section: Figure 12mentioning

confidence: 99%

Extension of line-splitting operation from graphs to binary matroids

Azanchiler

2008

Journal of Discrete Mathematical Sciences and Cryptography

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In this paper, we characterize the n-line splitting operation of graphs in terms of cycles of respective graphs and then extend this operation to binary matroids.In matroids, we call this operation as element-set splitting. For convenience, we call the resulting matroid, es-splitting matroid. We characterize circuits of es-splitting matroid. We also characterize the es-splitting matroid in terms of matrices.We also show that if M is a connected binary matroid then es-splitting matroid M e X is also connected.

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Determination of the bases of a splitting matroid

Cited by 17 publications

References 4 publications

A characterization of n-connected splitting matroids

A characterization of n-connected splitting matroids

On dual of the generalized splitting matroids

Extension of line-splitting operation from graphs to binary matroids

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