Geodesic
Extension of line-splitting operation from graphs to binary matroid
Lobachevskii journal of mathematics, Tome 24 (2006), pp. 3-12.

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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 an element-set splitting. The resulting matroid is called the es-splitting matroid. We characterize circuits of an es-splitting matroid. We also characterize the es-splitting matroid in terms of matrices. Also, we show that if $M$ is a connected binary matroid then the es-splitting matroid $M_X^e$ is also connected.
Keywords: binary matroid, $n$-line splitting, element-set splitting, connected matroid. 
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H. Azanchiler. Extension of line-splitting operation from graphs to binary matroid. Lobachevskii journal of mathematics, Tome 24 (2006), pp. 3-12. http://geodesic.mathdoc.fr/item/LJM_2006_24_a0/

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