Hamiltonian cycles in Cayley graphs of imprimitive 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.

Group Coding With Complex Isometries

“…One may instead use a restriction of the standard Cayley graph to determine an appropriate choice. (See Kriloff and Lay [15] for an analysis of Cayley graphs for G(r, 1, n).) Definition 22.…”

“…(Note that Kriloff and Lay [15] show existence of Hamiltonian cycles for the Cayley graphs of G(r, 1, n).) We use Remark 38 and the explicit decoding process described after Corollary 37.…”