A Characterization of the Bases of Line-Splitting Matroids

(Lobachevskii Journal of Mathematics, Volume XXVI)

In [1] the author extended n-line splitting from graphs to binary matroids and characterized the circuits of the result matroid, i.e. line-splitting matroid (es-splitting). In this paper, we characterize dependent, independent and base sets in line-splitting matroid M ^e_X. Moreover, we determine rank function of M ^e_X.