Geodesic
Graphic and Cographic Г-Extensions of Binary Matroids
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 4, pp. 889-898

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Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The Г-extension operation on binary matroids is a generalization of the point-addition operation. In general, under the Г-extension operation the properties like graphicness and cographicness of matroids are not preserved. In this paper, we obtain forbidden minor characterizations for binary matroids whose Г-extension matroids are graphic (respectively, cographic).
Keywords: splitting, Г-extension, graphic, cographic, minor 
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     author = {Borse, Y.M. and Mundhe, Ganesh},
     title = {Graphic and {Cographic} {{\CYRG}-Extensions} of {Binary} {Matroids}},
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Borse, Y.M.; Mundhe, Ganesh. Graphic and Cographic Г-Extensions of Binary Matroids. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 4, pp. 889-898. http://geodesic.mathdoc.fr/item/DMGT_2018_38_4_a1/