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.
- FindPlanarColoring[g] 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
open all close allBasic Examples (2)
Find a face coloring of the wheel graph:
FindPlanarColoring[WheelGraph[6]]Assign distinct colors to adjacent faces of a graph:
g = WheelGraph[6];FindPlanarColoring[g, ColorData[106, "ColorList"]]Graphics[GraphicsComplex[GraphEmbedding[g], Reverse@Table[Style[Polygon[PlanarFaceList[g][[i]]], %[[i]]], {i, Length[%]}]]]Scope (6)
FindPlanarColoring works with undirected graphs:
FindPlanarColoring[[image]]FindPlanarColoring[[image]]FindPlanarColoring[[image]]FindPlanarColoring[[image]]Use rules to specify the graph:
FindPlanarColoring[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2 -> 4}]Assign distinct colors to adjacent faces of a graph:
FindPlanarColoring[[image], ColorData[3, "ColorList"]]Properties & Relations (3)
Use PlanarFaceList to get the faces of planar graphs:
PlanarFaceList[[image]]Use DualPlanarGraph to get the dual of planar graphs:
DualPlanarGraph[[image]]A face coloring of a planar graph is a vertex coloring of its dual:
g = WheelGraph[6, VertexLabels -> Automatic]FindVertexColoring[DualPlanarGraph[g]]FindPlanarColoring[g]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