Minimum augmentation of a tree to a K‐edge‐connected graph
Shuichi Ueno, Yoji Kajitani, Hajime Wada · Networks · 1988
Abstract This paper solves the minimum augmentation problem for a given tree and positive integer k, that is, to make a tree k‐edge‐connected by adding the minimum number of edges. It is shown that the minimum number of edges is the least integer not less than a half of the deficiency of the tree which is defined as the sum of k‐(degree) over all the vertices whose degrees are less than k. The proof is constructive and gives a polynomial‐time algorithm for constructing such an augmentation.