The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) ...

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 a O(|V |) algorithm exists when G is a tree. In this paper a linear algorithm for 8nding HCN (L(G)) when G is a cactus is proposed. ? 2003 Elsevier B.V. All rights reserved.

In this paper we introduce an eecient algorithm for the on-line computation of the MacNeille completion of a poset. Our algorithm is polynomial in the number of elements in the lattice completion and has a better worst-case complexity than previous proposals.

We give the first algorithm for Matrix Completion that achieves running time and sample complexity that is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix. To the best of our knowledge, all previous algorithms either incurred a quadratic dependence on the condition number of the unknown matrix or a...