A forbidden-minor characterization for the class of regular matroids which yield the cographic es-splitting matroids

Shikare, M. M.; Dhotre, S. B.; Malavadkar, P. P.

doi:10.1134/s199508021302008x

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Several properties concerning es-splitting operation have been explored in [2,3,4,5,8]. The following proposition characterizes the circuits of the matroid M e X in terms of the circuits of the matroid M (see [2]).…”

Section: Properties Of Es-splitting Matroidsmentioning

confidence: 99%

The Closure Operator of es-Splitting Matroids

Dhotre,

Malavadkar,

Shikare

2016

Preprint

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The es-splitting operation for binary matroids is a natural generalization of Slater's n-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid M e X in terms of the closure operator of the original binary matroid M . We also characterize the flats of the es-splitting binary matroid M e X in terms of the flats of the original binary matroid M .

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Section: Properties Of Es-splitting Matroidsmentioning

confidence: 99%

The Closure Operator of es-Splitting Matroids

Dhotre,

Malavadkar,

Shikare

2016

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is intersting to observe that M e X \ γ and M e X \ {a, γ} are isomorphic with element splitting matroid and splitting matroid of M , respectively. The main theorems of this paper, Theorem 3.1 and Theorem 3.2 are motivated by a series of earlier work on splitting operation, element splitting operation and es-splitting operation [1,2,4,7,8,10,11,12,15,17].…”

Section: Introductionmentioning

confidence: 99%