FindPlanarColoring

finds a coloring with minimal size for the faces of the planar graph g.

FindPlanarColoring[g,{c1,c2,}]

finds a coloring {c1,c2,,ck} for the faces in the graph g.

Details and Options

• FindPlanarColoring is also known as graph coloring and face coloring.
• FindPlanarColoring is typically used for modeling scheduling and assignment problems.
• finds a coloring {c1,c2,,ck} with minimal size for the faces of g where ci are integers and ci is not equal to cj for two adjacent faces fi and fj of g with indices i and j.
• FindPlanarColoring[g,{c1,c2,}] uses the specified colors ci.
• FindPlanarColoring[g,l] is effectively equivalent to FindPlanarColoring[g,{1,2,,l}].

Examples

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Basic Examples(2)

Find a face coloring of the wheel graph:

Assign distinct colors to adjacent faces of a graph:

Visualize the graph:

Scope(6)

FindPlanarColoring works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Use rules to specify the graph:

Assign distinct colors to adjacent faces of a graph:

Properties & Relations(3)

Use PlanarFaceList to get the faces of planar graphs:

Use DualPlanarGraph to get the dual of planar graphs:

A face coloring of a planar graph is a vertex coloring of its dual:

Wolfram Research (2021), FindPlanarColoring, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPlanarColoring.html.

Text

Wolfram Research (2021), FindPlanarColoring, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPlanarColoring.html.

CMS

Wolfram Language. 2021. "FindPlanarColoring." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindPlanarColoring.html.

APA

Wolfram Language. (2021). FindPlanarColoring. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindPlanarColoring.html

BibTeX

@misc{reference.wolfram_2024_findplanarcoloring, author="Wolfram Research", title="{FindPlanarColoring}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/FindPlanarColoring.html}", note=[Accessed: 13-September-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_findplanarcoloring, organization={Wolfram Research}, title={FindPlanarColoring}, year={2021}, url={https://reference.wolfram.com/language/ref/FindPlanarColoring.html}, note=[Accessed: 13-September-2024 ]}