Splitting Off Operation for Binary Matroids and its Applications

Shikare, M. M.; Dalvi, Kiran; Dhotre, S. B.

doi:10.1007/s00373-010-1005-y

Cited by 8 publications

(19 citation statements)

References 7 publications

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“…For a given connected graph G, the matroid M (G) is Eulerian if and only if G is an Eulerian [6]. A matroid M is Eulerian if and only if M xy is Eulerian [3]. The next theorem, says that this property is preserved under 2-pinching operation.…”

Section: Applicationsmentioning

confidence: 96%

Generalization of pinching operation to binary matroids

Ghorbani

Azadi

Azanchiler

2020

Journal of Algebra Combinatorics Discrete Structures and Applications

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In this paper, we generalize the pinching operation on two edges of graphs to binary matroids and investigate some of its basic properties. For n ≥ 2, the matroid that is obtained from an n-connected matroid by this operation is a k-connected matroid with k ∈ {2, 3, 4} or is a disconnected matroid. We find conditions to guarantee this k. Moreover, we show that Eulerian binary matroids are characterized by this operation and we also provide some interesting applications of this operation.

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Section: Applicationsmentioning

confidence: 96%

Generalization of pinching operation to binary matroids

Ghorbani

Azadi

Azanchiler

2020

Journal of Algebra Combinatorics Discrete Structures and Applications

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“…In the following lemma, Shikare, Azadi and Waphare [8] characterized the rank function of the matroid M X in terms of the rank function of the matroid M . …”

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

confidence: 99%

“…We call a circuit of M as an OX-circuit if it contains an odd number of elements of the set X. Using Definition 1.2, Shikare, Azadi and Waphare [8] characterized the circuits of the splitting matroid M X .…”

Section: Introductionmentioning

confidence: 99%

A characterization of n-connected splitting matroids

Malavadkar

Shikare

Dhotre

2014

Asian-European J. Math.

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“…As an extension of this operation to binary matroids, Raghunathan, Shikare and Waphare [3] defined the splitting operation for binary matroids with respect to a pair of elements. The effects of the splitting operation on various parameters of a matroid like graphicness, cographicness, and connectedness have been well studied in the literature, for example, see [4][5][6]3,7,8].…”

Section: Introductionmentioning

confidence: 99%