On the structure of Hamiltonian cycles in Cayley graphs of finite quotients of the modular group

Abstract

It is a fairly longstanding conjecture that if G is any finite group with ¦G¦s > 2 and if X is any set of generators of G then the Cayley graph Γ( G : X) should have a Hamiltonian cycle. We present experimental results found by computer calculation that support the conjecture. It turns out that in the case where G is a finite quotient of the modular group the Hamiltonian cycles possess remarkable structural properties.