On the existence of a matching orthogonal to a 2-factorization

AbstractThis note gives a partial answer to a problem posed by Brian Alspach in a recent issue of Discrete Mathematics. We show that if F1, F2,…,Fd is a 2-factorization of a 2d-regular graph G of order n⩾3.23d then G contains a d-matching with exactly one edge from each of F1, F2,…,Fd