The obstructions for toroidal graphs with no $K_{3,3}$'s
arXiv:math/0411488 · doi:10.1016/j.disc.2007.12.075
Abstract
Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no $K_{3,3}$-subdivisions that coincide with the toroidal graphs with no $K_{3,3}$-minors. These graphs admit a unique decomposition into planar components and have short lists of obstructions. We provide the complete lists of four forbidden minors and eleven forbidden subdivisions for the toroidal graphs with no $K_{3,3}$'s and prove that the lists are sufficient.
10 pages, 7 figures, revised version with additional details