20.32 (2022)

(E. Rapaport Strasser). The Lovász conjecture states that a vertex-transitive connected graph is Hamiltonian. In the special case of Cayley graphs, one can ask the following. Consider a set $A$ which generates a group $G$ and is symmetric ($x \in A$ implies $x^{-1} \in A$). Is there a list $a_1, a_2, \dots, a_n$ of elements of $A$ such that $a_1, a_1 a_2, a_1 a_2 a_3, \dots, a_1 a_2 \dots a_n$ is a complete list of the elements of $G$?