One-Factorizations of Tensor Products of Graphs

A very natural question raised about products of graphs is the following. Do there exist necessary and sufficient conditions on a pair (G,H) of graphs for their product to have some specified property? In particular, for which graphs is the product one-factorizable? Sufficient conditions have been investigated for the cartesian, lexicographic, and tensor products in [3], [4], and [5]. However, the conditions for the tensor product to be one-factorizable are significantly more scanty than those for the other products. The purpose of this paper is to correct this situation somewhat.