Degree-bounded factorizations of bipartite multigraphs and of pseudographs

For d 1, s 0 a (d,d +s)-graph is a graph whose degrees all lie in the interval {d,d +1,...,d +s}. For r 1, a 0 an (r,r+1)-factor of a graph G is a spanning (r,r+a)-subgraph of G. An (r,r+a)-factorization of a graph G is a decomposition of G into edge-disjoint (r,r +a)-factors. We prove a number of results about (r,r+a)-factorizations of (d,d+s)-bipartite multigraphs and of (d,d + s)-pseudographs (multigraphs with loops permitted). For example, for t 1 let (r,s,a,t) be the least integer such that, if d (r,s,a,t) then every (d,d + s)-bipartite multigraph G has an (r,r + a)-factorization into x (r,r +a)-factors for at least t different values of x. Then we show that (r,s,a,t) = r tr +s-1 a +(t -1)r. Similarly, for t 1 let (r,s,a,t) be the least integer such that if d (r,s,a,t) then each (d,d + s)-pseudograph has an (r,r + a)-factorization into x (r,r + a)factors for at least t different values of x. We show that, if r and a are even, then (r,s,a,t) is given by the same formula. W...

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Anthony J. W. Hilton
• Keywords: Corresponding Functions, DM 2010, Simple Graphs, Tight Bounds