Graphic and Cographic Г-Extensions of Binary Matroids

Abstract

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
• 05b35
• 05c50
• 05c83