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.

10 pages, 7 figures, revised version with additional details

References in corpus (1)

• Characterization and enumeration of toroidal K_{3,3}-subdivision-free graphs

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