An algorithm is given that finds a cycle basis with the shortest possible length in $O(m^3 n)$ operations, which is the first known polynomial-time algorithm for this problem.Expand

An algorithm is given to solve the minimum cycle basis problem for regular matroids based upon Seymour's decomposition theorem, the Gomory-Hu tree, which is essentially the solution for cographicMatroids; and the corresponding result for graphs.Expand

This paper considers measurements using a distributed set of measurement points or beacons and proposes a relatively small candidate set of beacons for the current Internet topology, which has properties with relevant applications for all-paths routing on the public Internet and performance based routing.Expand

It is shown that if v is large enough, then an RBPD exists if and only if v ≡ k2 (modulo lcm(2k − 2, k), and that the categorical product of a k-factorable graph and a regular graph is also k- Factorable.Expand

Let S be a finite set of points in the plane. For each point x E S, let r, be the closest distance to any other point in the set, and let C, be the circle of radius r , centered at x. Toussaint has… Expand

The edge domination problem is NP-complete for planar bipartite graphs, their subdivision, line, and total graphs, perfect claw-free graphs, and planar cub...Expand

Abstract The main result of this paper is that for any pair of orthogonal Latin squares of side k, there will exist for all sufficiently large n a pair of orthogonal Latin squares with the first pair… Expand

The existence of a Room square of order 2n is known to be equivalent to the existence of two orthogonal one-factorizations of the complete graph on 2n vertices, where “orthogonal” means “any two… Expand