Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 17G / c / Solution

The Erdős-Stone theorem states precisely that, for every fixed graph $H$ with chromatic number $\chi (H)\ge 2$,If the bipartite graph $G$ has an edge, then $\chi (G)=2$. Substitution into the theorem givesIf $G$ has no edges, then every graph of sufficiently large order contains $G$ as a subgraph, so the conclusion is immediate.