A hereditary family $\mathcal{G}$ of graphs is $\chi$-bounded with $\chi$-binding function $f: \mathbb{N} \to \mathbb{N}$ if $\chi(G) \leq f(\omega(G))$ for all $G$ in $\mathcal{G}$. A classical result of Erdős shows that the gap between the clique number and the chromatic number of a graph can be arbitrarily large. Multiple interesting research questions arise from this result. The most prominent one asks: when is a family of graphs $\chi$-bounded?
The most famous construction that yields a triangle-free graph with an arbitrary large chromatic number is the Mycielskian construction. Obviously, a consequence of this result is that not all graph families are $\chi$-bounded. The Mycielskian contruction is therefore often used as a counterexample in this field of study. Thus, it would make sense to include this graph family as a static construction in Graphs.jl (staticgraphs.jl) and the Grötzsch graph (3rd Mycielskian) (in small graphs.jl).
I'd like to implement both in Graphs.jl, if there is nothing against it.
