A linear algorithm for the number of degree constrained subforests of a tree

Recent work of Farrell is concerned with determining the total number of ways in which one can cover the vertices of a tree T with vertex disjoint paths. Such path covers are spanning subforests in which each vertex is restricted to have degree at most two. If b: V(T)→N is a positive integer-valued function, then finding a b-matching is equivalent to finding a spanning subgraph in which the degree of each vertex v is at most b(v). A linear-time algorithm for determining the number of b-matching in a tree is presented.