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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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/

[1] H. Azanchiler, Г- extension of binary matroids, ISRN Discrete Math. 2011 (2011) Article ID 629707. doi:10.5402/2011/269707

[2] H. Azanchiler, On extension of graphic matroids, Lobachevskii J. Math. 36 (2015) 38–47. doi:10.1134/S1995080215010035

[3] Y.M. Borse, M.M. Shikare and K.V. Dalvi, Excluded-minor characterization for the class of cographic splitting matroids, Ars Combin. 115 (2014) 219–237.

[4] H. Fleischner, Eulerian Graphs and Related Topics, Part 1, Vol. 1 (North Holland, Amsterdam, 1990).

[5] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).

[6] T.T. Raghunathan, M.M. Shikare and B.N. Waphare, Splitting in a binary matroid, Discrete Math. 184 (1998) 267–271. doi:10.1016/S0012-365X(97)00202-1

[7] M.M. Shikare and B.N. Waphare, Excluded-minors for the class of graphic splitting matroids, Ars Combin. 97 (2010) 111–127.

[8] M.M. Shikare, G. Azadi and B.N. Waphare, Generalized splitting operation for binary matroids and its applications, J. Indian Math. Soc. (N.S.) 78 (2011) 145–154.

[9] P.J. Slater, A classification of 4-connected graphs, J. Combin. Theory Ser. B 17 (1974) 281–298. doi:10.1016/0095-8956(74)90034-3