Strasser’s conjecture on Hamiltonicity of Cayley graphs

Determine whether every connected Cayley graph is Hamiltonian.

Background

Cayley graphs are vertex-transitive and capture algebraic structure via group generators. Strasser (1959) conjectured that all connected Cayley graphs admit Hamilton cycles. While resolved for abelian groups, the general case remains open.

The paper resolves a random version of this conjecture (Theorem 1.8) via spectral expander Hamiltonicity but the full deterministic conjecture remains open.