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.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$G≔\mathrm{MirzakhaniGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 63\; vertices\; and\; 183\; edge(s)}$

$\mathrm{IsPlanar}\left(G\right)$

$\mathrm{true}$

$\mathrm{ChromaticNumber}\left(G\right)$

$3$

$\mathrm{DrawGraph}\left(G\right)$

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

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

For more information on Maple 2018 changes, see Updates in Maple 2018.