On graphic degree sequences and matching numbers

The sequence of prime gaps is graphic

“…One can ask, why should a suitable matching be found in G n ? Actually, this is not inconceivable, as the following theorem shows: Theorem 1.5 (Theorem 2.5 in [16]). Given a graphic sequence D of length n and an even integer 2 d n, the sequence D • d is graphic if and only if D has a realization with a matching of size d/2.…”