MirzakhaniGraph - Maple Help

GraphTheory[SpecialGraphs]

 MirzakhaniGraph
 construct Mirzakhani graph

 Calling Sequence MirzakhaniGraph()

Description

 • The MirzakhaniGraph() command returns the Mirzakhani graph, a 3-colorable planar graph with 63 vertices which is not 4-choosable.
 • The Mirzakhani graph is the smallest known graph satisfying these properties and was discovered by Maryam Mirzakhani in 1996.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $G≔\mathrm{MirzakhaniGraph}\left(\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 63 vertices and 183 edge\left(s\right)}}$ (1)
 > $\mathrm{IsPlanar}\left(G\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{ChromaticNumber}\left(G\right)$
 ${3}$ (3)
 > $\mathrm{DrawGraph}\left(G\right)$

References

 Mirzakhani, Maryam. A small non-4-choosable planar graph. Bull. Inst. Combin. Appl. 17 (1996), 15–18.

Compatibility

 • The GraphTheory[SpecialGraphs][MirzakhaniGraph] command was introduced in Maple 2018.