Let $G$ be the following Graph:
We want to decide whether for an input structure $\mathcal{S}$ there exists a homomorphism $S \to G$. We will call this problem $HOM_G$.
The task at hand is to show that $HOM_G$ is NP-complete. This is a bit strange since $HOM_G$ is not a general problem but a very specific one.
I've already made some observations: $HOM_G \in NP$ since if a potential homomorphism is given we can decide in polynomial time if it is correct. Furthermore all positive instances $\mathcal{S}$ have to be graphs because if there is a non-empty non-binary or more then one binary relation there is no homomorphism to $G$.
I'm a little bit stuck right now. Any ideas?