The obstructions for toroidal graphs with no $K_{3,3}$'s

Andrei Gagarin; Wendy Myrvold; John Chambers

doi:10.1016/j.disc.2007.12.075

The obstructions for toroidal graphs with no $K_{3,3}$'s

Combinatorics 2010-12-22 v2 Discrete Mathematics

Authors: Andrei Gagarin , Wendy Myrvold , John Chambers

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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.

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@article{arxiv.math/0411488,
  title  = {The obstructions for toroidal graphs with no $K_{3,3}$'s},
  author = {Andrei Gagarin and Wendy Myrvold and John Chambers},
  journal= {arXiv preprint arXiv:math/0411488},
  year   = {2010}
}

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10 pages, 7 figures, revised version with additional details

The obstructions for toroidal graphs with no $K_{3,3}$'s

Abstract

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