We prove that the property to be limit aperiodic is preserved by the standard construction with groups like extension, HNN extension and free product. We also construct a non-limit aperiodic G-space.

This paper describes four years of experience designing and teaching a project-centered course in collaborative computing that seeks to integrate new experiences into the MIS curriculum. The course grew out of our desire to expose students to collaborative computing in a fashion that we hope will help them to bridge their knowledge from the classroom to the realities they will face throughout t...

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silen...

In this paper, we consider the independent dominating set polytope. We give a complete linear description of that polytope when the graph is reduced to a cycle. This description uses a general class of valid inequalities introduced in [T.M. Contenza, Some results on the dominating set polytope, Ph.D. Dissertation, University of Kentucky, 2000]. We devise a polynomial time separation algorithm f...

An (α, β)-spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u, v, dH(u, v) ≤ α ·dG(u, v)+β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α, β)-spanner H for a given graph G and distortion parameters α and β. It first presents a generic distr...

A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. For k 1 = ::: = kn = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number found then the notion of k-dominating ...

A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen.