Mycielski is a graph construction which, given a graph G on $n$ vertices, returns a graph on $2n+1$ vertices. If G is triangle-free with chromatic number $k$, then the returned graph is triangle-free with chromatic number $k+1$.

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

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

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

$P≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$G≔\mathrm{Mycielski}\left(P\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 21\; vertices\; and\; 55\; edge(s)}$

$\mathrm{ChromaticNumber}\left(G\,'\mathrm{bound}'\right)$

$3..4$

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

$4$