Splitting Operation and Connectedness in Binary Matroids

The splitting operation on an n-connected binary matroid may not yield an n-connected binary matroid. In this paper, we characterize n-connected binary matroids which yield n-connected binary matroids by the generalized splitting operation.

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Some Results Involving the Splitting Operation on Binary Matroids

ISRN Discrete Mathematics ◽

10.5402/2012/406147 ◽

2012 ◽

Vol 2012 ◽

pp. 1-8

Author(s):

Naiyer Pirouz ◽

Maruti Mukinda Shikare

Keyword(s):

Binary Matroids ◽

Splitting Operation

We obtain some results concerning the planarity and graphicness of the splitting matroids. Further, we explore the effect of splitting operation on the sum of two matroids.

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On 3-connected es-splitting binary matroids

Asian-European Journal of Mathematics ◽

10.1142/s1793557116500170 ◽

2016 ◽

Vol 09 (01) ◽

pp. 1650017 ◽

Cited By ~ 1

Author(s):

S. B. Dhotre ◽

P. P. Malavadkar ◽

M. M. Shikare

Keyword(s):

Sufficient Condition ◽

Binary Matroid ◽

Binary Matroids ◽

Splitting Operation

The es-splitting operation on a [Formula: see text]-connected binary matroid may not preserve the [Formula: see text]-connectedness of the matroid. In this paper, we provide a sufficient condition for a [Formula: see text]-connected binary matroid to yield a [Formula: see text]-connected binary matroid under the es-splitting operation. We derive a splitting lemma for [Formula: see text]-connected binary matroids as an application of this result.

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Γ-Extension of Binary Matroids

ISRN Discrete Mathematics ◽

10.5402/2011/629707 ◽

2011 ◽

Vol 2011 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Habib Azanchiler

Keyword(s):

Binary Matroids ◽

Splitting Operation ◽

Element Addition ◽

The Given ◽

Special Case

We extend the notion of a point-addition operation from graphs to binary matroids. This operation can be expressed in terms of element-addition operation and splitting operation. We consider a special case of this construction and study its properties. We call the resulting matroid of this special case a Γ-extension of the given matroid. We characterize circuits and bases of the resulting matroids and explore the effect of this operation on the connectivity of the matroids.

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A characterization of a class of non-binary matroids

Journal of Combinatorial Theory Series B ◽

10.1016/0095-8956(90)90025-u ◽

1990 ◽

Vol 49 (2) ◽

pp. 181-189 ◽

Cited By ~ 9

Author(s):

James G Oxley

Keyword(s):

Binary Matroids

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On Minimally 3-Connected Binary Matroids

Combinatorics Probability Computing ◽

10.1017/s0963548301004850 ◽

2001 ◽

Vol 10 (5) ◽

pp. 453-461 ◽

Cited By ~ 4

Author(s):

TALMAGE JAMES REID ◽

HAIDONG WU

Keyword(s):

Binary Matroids ◽

Connected Graphs

We generalize a minimal 3-connectivity result of Halin from graphs to binary matroids. As applications of this theorem to minimally 3-connected matroids, we obtain new results and short inductive proofs of results of Oxley and Wu. We also give new short inductive proofs of results of Dirac and Halin on minimally k-connected graphs for k ∈ {2,3}.

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