3 Centralized CDS Construction 335 3.1 Guha and Khuller’s Algorithm . . . . . . . . . . . . . . . . . . . . . 336 3.2 Ruan’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 3.3 Cheng’s Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 340 3.4 Min’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 3.5 Butenko’s Algorithm . . . . . . ....

If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number γc(G) of G. A graph G is called a perfect connected-dominant graph if γ(H) = γc(H) for each connected induced subgraph H of G. We prove that a graph is a perfect connected-dominant graph if and only i...

An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighl.)ourhood of the third. Graphs that do not. co~,tain an asteroidal triple are called asteroidal triple-free (AT-free) graphs. AT-free graphs strictly contain the well-known class of cocomparability graphs, and are not necessarily perfect.. We present efficient,...

In this paper empirical tests for the overreaction and underreaction hypothesis in the Brazilian stock market are presented. For these tests, due to the complexity of these phenomena, a new model based on the fuzzy set theory is proposed. It is shown that such model is strongly connected with two heuristics of behavioral finance: representativeness and anchoring. The proposed model is used to f...

Let G be a connected graph with vertex set V (G). A set S of vertices in G is called a weakly connected dominating set of G if (i) S is a dominating set of G and (ii) the graph obtained from G by removing all edges joining two vertices in V (G) \ S is connected. A weakly connected dominating set S of G is said to be minimum or a γw-set if |S| is minimum among all weakly connected dominating set...

A graph G is 3-domination-critical (3-critical, for short), if its domination number γ is 3 and the addition of any edge decreases γ by 1. In this paper, we show that every 3-critical graph with independence number 4 and minimum degree 3 is Hamilton-connected. Combining the result with those in [2], [4] and [5], we solve the following conjecture: a connected 3critical graph G is Hamilton-connec...

A vertex subset S in a graph G is a dominating set if every vertex not contained in S has a neighbor in S. A dominating set S is a connected dominating set if the subgraph G[S] induced by S is connected. A connected dominating set S is a minimal connected dominating set if no proper subset of S is also a connected dominating set. We prove that there exists a constant ǫ > 10 such that every grap...

This paper addresses the scatternet formation for large scale multi-hop Bluetooth networks. We first describe an efficient method to build a Connected Dominating Set (CDS) as the backbone of multi-hop Bluetooth network, then propose new algorithms to form the dBBlue scatternets (Song et al., 2005) in each cluster. The final scatternet, M-dBBlue, guarantees the connectivity. Our experiment shows...