Minimum cutsets in hypercubes

Minimum Feedback Vertex Set in k - Dimensional Hypercubes Riccardo

In this paper we nd upper and lower bounds to the size of the feedback vertex set for k-dimensional hypercubes. Given a graph, the minimum feedback vertex set problem consists of nding a subset of vertices of minimum size whose removal induces an acyclic subgraph. The problem is NP-hard for general networks 2], but interesting polynomial solutions have been found for particular

Minimum Feedback Vertex Set in k-Dimensional Hypercubes

Galaxy cutsets in graphs

Given a network G = (V,E), we say that a subset of vertices S ⊆ V has radius r if it is spanned by a tree of depth r. We are interested in determining whether G has a cutset that can be written as the union of k sets of radius r. This generalizes the notion of k-vertex connectivity, since in the special case r = 0, a set spanned by a tree of depth r is a single vertex. Our motivation for consid...

Minimum wirelength of hypercubes into n-dimensional grid networks

In the paper [Exact wirelength of hypercube on a grid, Discrete Applied Mathematics, 157 (2009), no. 7, 1486 1495], the minimum wirelength of an -dimensional hypercube into a 2b2c £ 2d2e grid has been obtained. In this paper, we obtain the same when the 2b2c £ 2d2e rectangular grid is replaced by a generalized grid of size 21 £ 22 £ ¢ ¢ ¢ £ 2 where 1 + 2 + +  = , 1 · 2 · ¢ ¢...

Cutsets of Boolean lattices

In graph theory, Menger’s Theorem is the basis of many results concerning notions of connectedness. There are many versions, in this paper the following will be useful. Let G = (V, E) be a directed graph and A, B disjoint subsets of V with no directed edge from A to B. A subset of V -A U B is called an (A, B) separating vertex-set if every directed path from A to B intersects F. A set of direct...