Graphs that admit square 1-factorizations are hamiltonian Cayley graphs

Abstract

A square 1-factorization of a graph is a 1-factorization in which the union of any two distinct 1-factors is a disjoint union of 4-cycles. We show that a graph admits a square 1-factorization if and only if it is a Cayley graph with group (ℤ2)n for somen. The rest of the title follows since Cayley graphs of abelian groups are known to be hamiltonian.