Cayley graphs are Hamiltonian

Statement
This conjecture was made by Lovasz and is still open.

Let $$G$$ be a finite group and $$S$$ be any generating set for $$G$$. Then, the Cayley graph of $$G$$ with respect to $$S$$ is a Hamiltonian graph -- in other words, it has a Hamiltonian cycle, a cycle that visits every vertex exactly once.