Abstract: One of the more famous open conjectures in graph factorization is the 1-factorization Conjecture, which states that the edges of any k-regular graph of even order n can be decomposed into k 1-factors if k n/2. This conjecture has been traced back to the 1950's.
In the 1980's, Chetwynd and Hilton, and independently Niessen, showed the conjecture is true if k [(sqrt(7) - 1)/2]n (that is about 0.823 n). We will outline that approach (joint work with Hilton), and talk about a variation that could lower that coefficient.