Abstract: A (d,d+1)-graph is a graph whose degrees all lie in the set {d,d+1}. Such a graph is also called semiregular. An (r,r+1)-factor in a graph is a spanning subgraph which is itself an (r,r+1)-graph. A decomposition of a graph into edge-disjoint (r,r+1)-factors is called an (r,r+1)-factorization.
I shall discuss the general question of which graphs have an (r,r+1)-factorization and I shall also consider the question of how many (r,r+1)-factors there can be in an (r,r+1)-factorization of some given graph G.