Coloring graphs with crossings
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 K6 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. © 2008 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Oporowski, B., & Zhao, D. (2009). Coloring graphs with crossings. Discrete Mathematics, 309 (9), 2948-2951. https://doi.org/10.1016/j.disc.2008.07.040