1-factorisation of the Composition of Regular Graphs

1-factorability of the composition of graphs is studied. The followings sufficient conditions are proved: is 1-factorable if and are regular and at least one of the following holds: (i) Graphs and both contain a 1-factor, (ii) is 1-factorable (iii) is 1-factorable. It is also shown that the tensor product is 1-factorable, if at least one of two graphs is 1-factorable. This result in turn implies that the strong tensor product is 1-factorable, if is 1-factorable.