In their paper [DT1], N. Dunfield and W. Thurston define a notion of “random 3-manifold” and study some properties of those manifolds with respect (among other things) to the existence of finite covers with certain covering groups, especially with regard to their homological properties (in particular, which ones have positive first Betti number). In this note, we show that some applications of ...

Let G be a graph. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we would like to characterize the cubic graphs with total domatic number at least two.

Let s be an integer, f = f(n) a function, and H a graph. Define the Ramsey-Turán number RTs(n,H, f) as the maximum number of edges in an H-free graph G of order n with αs(G) < f , where αs(G) is the maximum number of vertices in a Ks-free induced subgraph of G. The Ramsey-Turán number attracted a considerable amount of attention and has been mainly studied for f not too much smaller than n. In ...

An induced subgraph is called homogeneous if it is either a clique or an independent set. Let hom(G) denote the size of the largest homogeneous subgraph of a graph G. In this short paper we study properties of graphs on n vertices with hom(G) ≤ C log n for some constant C. We show that every such graph contains an induced subgraph of order αn in which β √ n vertices have different degrees, wher...

The cube graph Qn is the skeleton of the n-dimensional cube. It is an n-regular graph on 2 n vertices. The Ramsey number r(Qn,Ks) is the minimum N such that every graph of order N contains the cube graph Qn or an independent set of order s. In 1983, Burr and Erdős asked whether the simple lower bound r(Qn,Ks) ≥ (s − 1)(2n − 1) + 1 is tight for s fixed and n sufficiently large. We make progress ...

For an l-graph G, the Turán number ex(n,G) is the maximum number of edges in an n-vertex l-graph H containing no copy of G. The limit π(G) = limn→∞ ex (n,G)/ ( n l ) is known to exist [8]. The Ramsey-Turán density ρ(G) is defined similarly to π(G) except that we restrict to only those H with independence number o(n). A result of Erdős and Sós [3] states that π(G) = ρ(G) as long as for every edg...

We study a function on graphs, denoted by Gamma , representing vectorially the domination number of a graph, in a way similar to that in which the Lovász Theta function represents the independence number of a graph. This function is a lower bound on the homological connectivity of the independence complex of the graph, and hence is of value in studying matching problems by topological methods. ...

AIM The high variability of "centre-specific" documentation required by Independent Ethics Committee (IEC) plays a role in the time required for activation of participating centres of multicentre clinical trials. This study (a) provides a picture of the different activities, structural requirements and resources dedicated to the operation of the local IEC in Italy; (b) defines a detailed list o...