The obstructions for toroidal graphs with no K 3,3 's
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.