This paper addresses the following questions for a given tree T and integer
d≥2: (1) What is the minimum number of degree-d subtrees that partition
E(T)? (2) What is the minimum number of degree-d subtrees that cover
E(T)? We answer the first question by providing an explicit formula for the
minimum number of subtrees, and we describe a linear time algorithm that finds
the corresponding partition. For the second question, we present a polynomial
time algorithm that computes a minimum covering. We then establish a tight
bound on the number of subtrees in coverings of trees with given maximum degree
and pathwidth. Our results show that pathwidth is the right parameter to
consider when studying coverings of trees by degree-3 subtrees. We briefly
consider coverings of general graphs by connected subgraphs of bounded degree