Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649900 | Discrete Mathematics | 2009 | 4 Pages |
Abstract
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 K6K6 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Bogdan Oporowski, David Zhao,