Abstract
An elementary lift of a binary matroid M that arises from a binary coextension of M can easily be obtained by applying the splitting operation on M. This operation on a graphic matroid may not produce a graphic matroid. We give a method to determine the forbidden minors for the class of graphic matroids M such that the splitting of M by any set of k elements is again a graphic matroid. Using this method, we obtain such minors for k=2,3,4. One may compute such minors for k≥5. As a consequence, we obtain the forbidden minors for the class of graphic matroids whose all elementary lifts obtained via binary coextensions are also graphic. There are six such graphic minors.
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