Asymptotic enumeration of labeled multigraphs by vertices,edges, and degree parities

We show that the number of labeled (n, q)-multigraphs with some specified p vertices of odd degree is asymptotically independent of p and is in fact asymptotically 2^1?n times the number of (n, q)-multigraphs. We determine the asymptotic number of (n, q)-multigraphs.