A linear algorithm for the Hamiltonian completion number of a tree

Given a graph G = (V , E ), HCN (L(G)) is the minimum number of edges to be added to its line graph L(G) to make L(G) Hamiltonian. This problem is known to be NP-hard for general graphs, whereas an O(|V |5) algorithm exists when G is a tree. In this paper a linear algorithm for finding HCN(L(G)) when G is a tree is proposed. 2001 Elsevier Science B.V. All rights reserved