usecached : keyword option of the form usecached=true or usecached=false.

Specifies whether previously stored information should be used, if available. The default is true.

The IsPerfectGraph(G) command returns true if G is a perfect graph and false otherwise.

An undirected graph G is perfect if in every subgraph of G, the chromatic number is equal to the clique number.

Split graphs are closed under graph complement.

Every chordal graph is a perfect graph.

Every split graph is a perfect graph.

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

$\mathrm{C5}≔\mathrm{CycleGraph}\left(5\right)$

$\mathrm{C5}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 5\; edge(s)}$

$\mathrm{IsPerfectGraph}\left(\mathrm{C5}\right)$

$\mathrm{false}$

$\mathrm{K5}≔\mathrm{CompleteGraph}\left(5\right)$

$\mathrm{K5}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 10\; edge(s)}$

$\mathrm{IsPerfectGraph}\left(\mathrm{K5}\right)$

$\mathrm{true}$

$P≔\mathrm{SpecialGraphs}:-\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{IsPerfectGraph}\left(P\right)$

$\mathrm{false}$

The GraphTheory[IsPerfectGraph] command was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.