The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid

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Binary Matroid, es-splitting operation, closure operator, ats, hyperplanes
Primary, 05B35


The es-splitting operation on 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 MeX in terms of the closure operator of the original binary matroid M. We also describe the ats and the hyperplanes of the es-splitting bi- nary matroid MeX in terms of the ats and the hyperplanes, respectively of the original binary matroid M.


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How to Cite

Malavadkar, P. P., Dhotre, S. B., & Shikare, M. M. (2021). The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid. The Journal of the Indian Mathematical Society, 88(3-4), 334–345.
Received 2021-05-19
Accepted 2021-05-19
Published 2021-06-14



Habib Azanchiler, Extension of line-splitting operation from graphs to binary matroid, Lobachevskii J. Math., 24. (2006), 3-12.

Habib Azanchiler, A characterization of the bases of line-splitting matroids, Lobachevskii J. Math., 26. (2007), 5-15.

S. B. Dhotre, P. P. Malavadkar and M. M. Shikare, On 3-connected es-splitting binary matroids, Asian-European J. Math., 9. (1)(2016), 1650017-26.

S. Hedetniemi, Characterizations and constructions of minimally 2-connected graphs and minimally strong digraphs, Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (1971), 257-282.

P. P. Malavadkar, M. M. Shikare and S. B. Dhotre, A characterization of n-connected splitting matroids, Asian-European J. Math., 7. (4)(2014), 1-7.

P. P. Malavadkar, M. M. Shikare and S. B. Dhotre, A characterization of cocircuits of an es-splitting matroid, J. Comb. Math. Comb. Comput., 105. (2018), 247-258.

P. P. Malavadkar, S. B. Dhotre and M. M. Shikare, Forbidden-minors for the class of cographic maroids which yield the graphic element splitting matroids, Southeast Asian Bull. Math., 43. (1)(2019), 105-119.

Oxley J. G., Matroid Theory, Oxford University Press, Oxford 1992.

T. T. Raghunathan, M. M. Shikare and B. N. Waphare, Splitting in a binary matroid, Discrete Mathematics, 184. (1998), 267-271.

M. M. Shikare, G. Azadi and B. N. Waphare, Generalized splitting operation for binary matroids and applications, J. Indian Math. Soc., 78. (1-4)(2011), 145-154.

M. M. Shikare, S. B. Dhotre and P. P. Malavadkar, A forbidden-minor characteriza- tion for the class of regular matroids which yield the cographic es-splitting matroids, Lobachevskii J. of Math., 34. (2013), 173-180.

P. J. Slater, A Classi cation of 4-connected graphs, J. Combin. Theory, 17. (1974), 282-298.

W. T. Tutte, Lectures on matroids, J. Res. Nat. Bur. Standards, B69. (1965), 1-47.

W. T. Tutte, A theory of 3-connected graphs, Indag. Math., 23. (1961), 441-455.

W. T. Tutte, Connectivity in matroids, Canad. J. Math., 18. (1966), 1301-1324.