Binary signed-graphic matroids: Representations and recognition algorithms

Recognition algorithms determining whether a given matroid is binary signed-graphic or not are presented in this work. Depending on whether the input is a cographic, a binary or a general matroid different algorithms are provided utilizing mainly decomposition results for the class of signed-graphic matroids. Finally, in order to devise such algorithms, necessary results regarding the representability of signed-graphic matroids in various fields are also given.