On 1-factorizability of Cayley graphs
The author proves the existence of a 1-factorization of the undirected Cayley graph for all generating sets of even order Abelian, dihedral and dicyclic groups. The result is also shown for minimal generating sets in even order nilpotent groups, the direct product of a dihedral and a cyclic group, and other special cases. These results considerably improve the result of \textit{G. Stern} and \textit{H. Lenz} [Steiner triple systems with given subspaces, Boll. Unione Mat. Ital., V. Ser., A 17, 109-114 (1980; Zbl 0501.05012)] for even order cyclic groups, and provide strong evidence to support the conjecture that all Cayley graphs of groups of even order have a 1-factorization.
scientific article; zbMATH DE number 3929039
scientific article