The Algorithmic Complexity of Bondage and Reinforcement Problems in bipartite graphs

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$, denoted by $\gamma(G)$, is the smallest cardinality of a dominating set of $G$. The bondage number of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number larger than $\gamma(G)$. The reinforcement number of $G$ is the smallest number of edges whose addition to $G$ results in a graph with smaller domination number than $\gamma(G)$. In 2012, Hu and Xu proved that the decision problems for the bondage, the total bondage, the reinforcement and the total reinforcement numbers are all NP-hard in general graphs. In this paper, we improve these results to bipartite graphs.Comment: 13 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1109.1657; and text overlap with arXiv:1204.4010 by other author

Bondage number of grid graphs

The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.Comment: 13 pages. Discrete Applied Mathematics, 201

The bondage number of random graphs

A dominating set of a graph is a subset $D$ of its vertices such that every vertex not in $D$ is adjacent to at least one member of $D$. The domination number of a graph $G$ is the number of vertices in a smallest dominating set of $G$. The bondage number of a nonempty graph $G$ is the size of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. In this note, we study the bondage number of binomial random graph $G(n,p)$. We obtain a lower bound that matches the order of the trivial upper bound. As a side product, we give a one-point concentration result for the domination number of $G(n,p)$ under certain restrictions

Trafficking of Migrant Workers from Romania: Issues of Labor and Sexual Exploitation

Part of a major research project on the forms of forced labor today developed by the ILO Special Action Programme to Combat Forced Labour (SAP-FL), this paper argues that trafficking for labor exploitation is an emerging issue in Europe and in particular in Romania. Features a detailed comparison of living conditions prior to the emergence of immigration, trafficking, and/or forced labor

Slavery is bad for business: analyzing the impact of slavery on national economies

Public discourse on human trafficking and modern-day slavery is reaching a tipping point -- it is coming to be understood as a global problem with economic and policy implications far beyond simple reports of cross-border human trafficking. A decade ago most educated citizens considered slavery a phenomenon of the past, relegated to history textbooks. Today a strong narrative has reached global proportions: activists, epistemic communities, NGOs, IGOs, and governments are acknowledging the scope and extent of slavery in the twenty-first century. One need only point to Nicholas Kristof and Sheryl Wu Dunn’s bestseller Half the Sky, President Barack Obama’s 2012 speech at the Clinton Global Intiative, or the awareness that celebrities such as Mira Sorvino and Jada Pinkett Smith are raising about the subject to illustrate how far the antislavery movement has progressed.1 Yet despite such civic mindedness, surprisingly little data and empirically driven research exist on slavery today. Although some headway has been made in estimating its prevalence -- most notably in the form of contributions by Kevin Bales and by the International Labor Organization (ILO) -- apart from a rough estimate of how many slaves exist in the world today (21 to 27 million), scholars and policy makers know little about the risk factors -- let alone the business impact -- that contemporary slavery has on the global community.2 Indeed, most extant research, although useful, is qualitative, not allowing for statistical models.3 To what extent is slavery empirically bad for business? For whom is the business of slavery profitable, and for whom is it economically burdensome