Relations between packing and covering numbers of a tree

Abstract

Let Pk denote the size of the largest subset of nodes of a tree T with n nodes such that the distance between any two nodes in the subset is at least k + 1; let Ckdenote the size of the smallest subset of nodes of T such that every node of T is at distance at most k from some node in the subset. We determine various relations involving Pk and Ck; in particular, we show that Pk + kCk ≦n if n≧k + l and that Pzk = Ck. © 1975 Pacific Journal of Mathematics.