The MarkstroemGraph() command returns the Markström graph, a planar undirected graph with 15 vertices and 39 edges.

The Markstroem graph was discovered by Klas Markström as a counterexample to the open Erdős-Gyárfás conjecture.

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

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 24\; vertices\; and\; 36\; edge(s)}$

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

$\mathrm{true}$

$\mathrm{DrawGraph}\left(G\,\mathrm{style}=\mathrm{planar}\right)$

"Markstroem graph", Wikipedia. http://en.wikipedia.org/wiki/Erdős–Gyárfás conjecture

The GraphTheory[SpecialGraphs][MarkstroemGraph] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.