Geodesic
Forbidden-minor characterization for the class of cographic element splitting matroids
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 601-606

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In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K₄).
Keywords: binary matroid, graphic matroid, cographic matroid, minor 
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     title = {Forbidden-minor characterization for the class of cographic element splitting matroids},
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Dalvi, Kiran; Borse, Y.; Shikare, M. Forbidden-minor characterization for the class of cographic element splitting matroids. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 601-606. http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a13/