Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups

TL;DR

This paper proves that Cayley graphs of imprimitive complex reflection groups have Hamiltonian cycles, supporting the broader conjecture that all finite groups' Cayley graphs possess such cycles.

Contribution

It extends known results from real reflection groups to imprimitive complex reflection groups, confirming the Hamiltonian cycle existence in this broader class.

Findings

Cayley graphs of imprimitive complex reflection groups have Hamiltonian cycles.

Supports the conjecture that all finite groups' Cayley graphs have Hamiltonian cycles.

Generalizes previous results from real to complex reflection groups.

Abstract

Generalizing a result of Conway, Sloane, and Wilkes for real reflection groups, we show the Cayley graph of an imprimitive complex reflection group with respect to standard generating reflections has a Hamiltonian cycle. This is consistent with the long-standing conjecture that for every finite group, G, and every set of generators, S, of G the undirected Cayley graph of G with respect to S has a Hamiltonian cycle.