Habib Azanchiler

Extension of Line-splitting Operation from Graphs to Binary Matroid

(Lobachevskii Journal of Mathematics, Vol.24, pp.3-12 )

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 eX is also connected.



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