FranklinGraph
returns a 12-vertex graph that represents a 6-chromatic map on the Klein bottle. It is the sole counterexample to Heawood's map-coloring conjecture.


FranklinGraph
FranklinGraph
returns a 12-vertex graph that represents a 6-chromatic map on the Klein bottle. It is the sole counterexample to Heawood's map-coloring conjecture.
Details and Options
- FranklinGraph functionality is now available in the built-in Wolfram Language function GraphData.
- To use FranklinGraph, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
See Also
Tech Notes
Related Guides
-
▪
- Built-in Graphs ▪
- Graphs & Networks ▪
- Graph Visualization ▪
- Computation on Graphs ▪
- Graph Construction & Representation ▪
- Graphs and Matrices ▪
- Graph Properties & Measurements ▪
- Graph Operations and Modifications ▪
- Statistical Analysis ▪
- Social Network Analysis ▪
- Graph Properties ▪
- Mathematical Data Formats ▪
- Discrete Mathematics
Text
Wolfram Research (2012), FranklinGraph, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/FranklinGraph.html.
CMS
Wolfram Language. 2012. "FranklinGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/FranklinGraph.html.
APA
Wolfram Language. (2012). FranklinGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/FranklinGraph.html
BibTeX
@misc{reference.wolfram_2025_franklingraph, author="Wolfram Research", title="{FranklinGraph}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/FranklinGraph.html}", note=[Accessed: 09-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_franklingraph, organization={Wolfram Research}, title={FranklinGraph}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/FranklinGraph.html}, note=[Accessed: 09-August-2025]}