On cographic matroids and signed-graphic matroids Original Research Article

We prove that a connected cographic matroid of a graph image is the bias matroid of a signed graph image iff image imbeds in the projective plane. In the case that image is nonplanar, we also show that image must be the projective-planar dual signed graph of an actual imbedding of image in the projective plane. As a corollary we get that, if image denote the 29 nonseparable forbidden minors for projective-planar graphs, then the cographic matroids of image 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.