The GroetzschGraph() command returns the Grötzsch graph, a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5.

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

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 11\; vertices\; and\; 20\; edge(s)}$

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

$\mathrm{false}$

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

"Grötzsch graph", Wikipedia. http://en.wikipedia.org/wiki/Groetzsch_graph