• Corpus ID: 6854309

Coloring graphs using topology

@article{Knill2014ColoringGU,
  title={Coloring graphs using topology},
  author={Oliver Knill},
  journal={ArXiv},
  year={2014},
  volume={abs/1412.6985}
}
  • O. Knill
  • Published 22 December 2014
  • Mathematics
  • ArXiv
Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if all interior edge degrees are even. Using a refinement process which cuts the interior along surfaces we can adapt the degrees along the boundary of that surface. More efficient is a self-cobordism of G with itself with a host graph discretizing the product… 
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