Y.M. Borse, G. Mundhe
Graphic and cographic Γ-extensions of binary matroids
Discussiones Mathematicae Graph Theory
Received 12.10.2016, Revised 02.03.2017, Accepted 02.03.2017, doi: 10.7151/dmgt.2043
Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The Γ-extension operation on binary matroids is a generalization of the point-addition operation. In general, under the Γ-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 Γ-extension matroids are graphic (respectively, cographic).
splitting, Γ-extension, graphic, cographic, minor