The obstructions for toroidal graphs with no $K_3,3$'s
<|reference_start|>The obstructions for toroidal graphs with no $K_3,3$'s: 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.<|reference_end|>
@article{gagarin2004the,
    title={The obstructions for toroidal graphs with no $K_{3,3}$'s},
    author={Andrei Gagarin, Wendy Myrvold, and John Chambers},
    journal={Discrete Math. 309 (2009), no. 11, pp. 3625-3631},
    year={2004},
    doi={10.1016/j.disc.2007.12.075},
    archivePrefix={arXiv},
    eprint={math/0411488},
    primaryClass={math.CO cs.DM}
}