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

摘要

Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no K-3,K-3-subdivisions that coincide with the toroidal graphs with no K-3,K-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,K-3's and prove that the lists are sufficient.