Coloring graphs with crossings

Details Coloring graphs with crossings Coloring graphs with crossings

2005-01-25

arxiv.org/abs/math/0501427v1

Mathematics

Combinatorics

5 pages

Scientific paper

We generalize the Five Color Theorem by showing that it extends to graphs
with two crossings. Furthermore, we show that if a graph has three crossings,
but does not contain K_6 as a subgraph, then it is also 5-colorable. We also
consider the question of whether the result can be extended to graphs with more
crossings.

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