usecached : keyword option of the form usecached=true or usecached=false. This specifies whether a previously stored clique number should be used, if available. The default is true.

The IsTriangleFree(G) command returns true if G is a triangle-free graph and false otherwise.

An undirected graph G is triangle-free if it does not contain any cycle of length 3. This is equivalent to stating the clique number of G is less than 3.

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

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

$G≔\mathrm{Graph}\left(\left\{\left\{1\,2\right\}\,\left\{2\,3\right\}\,\left\{3\,1\right\}\,\left\{3\,4\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

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

$\mathrm{false}$

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

$P≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

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

$\mathrm{true}$

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

$C≔\mathrm{ClebschGraph}\left(\right)$

$C≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 16\; vertices\; and\; 40\; edge(s)}$

$\mathrm{IsTriangleFree}\left(C\right)$

$\mathrm{true}$

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

The GraphTheory[IsTriangleFree] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.