On cographic matroids and signed-graphic matroids

Abstract: We prove that a connected cographic matroid of a graph is the bias matroid of a signed graph iff imbeds in the projective plane. In the case that is nonplanar, we also show that must be the projective-planar dual signed graph of an actual imbedding of in the projective plane. As a corollary we get that, if denote the 29 nonseparable forbidden minors for projective-planar graphs, then the cographic matroids of are among the forbidden minors for the class of bias matroids of signed graphs. We will obtain other structural results about bias matroids of signed graphs along the way. [Copyright &y& Elsevier]