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

Independent Domination Of Subcubic Graphs

Let G be a simple graph. The independent domination number i(G) is the minimum cardinality among all maximal independent sets of G. A graph is subcubic whenever the maximum degree is at most three. In this paper, we will show that the independent domination number of a connected subcubic graph of order n having minimum degree at least two is at most 3(n+1)/7, providing a sharp upper bound for subcubic connected graphs with minimum degree at least two

A novel approach to study realistic navigations on networks

We consider navigation or search schemes on networks which are realistic in the sense that not all search chains can be completed. We show that the quantity $\mu = \rho/s_d$, where $s_d$ is the average dynamic shortest distance and $\rho$ the success rate of completion of a search, is a consistent measure for the quality of a search strategy. Taking the example of realistic searches on scale-free networks, we find that $\mu$ scales with the system size $N$ as $N^{-\delta}$, where $\delta$ decreases as the searching strategy is improved. This measure is also shown to be sensitive to the distintinguishing characteristics of networks. In this new approach, a dynamic small world (DSW) effect is said to exist when $\delta \approx 0$. We show that such a DSW indeed exists in social networks in which the linking probability is dependent on social distances.Comment: Text revised, references added; accepted version in Journal of Statistical Mechanic

Participatory Statistics to Measure Prevalence in Bonded Labour Hotspots in Uttar Pradesh and Bihar: Findings of the Base- and EndLine Study

This report documents the findings of the Institute of Development Studies’(IDS) and its partner, Praxis Institute for Participatory Practices’, programme of research, learning and evaluation of the Freedom Fund funded operational work in a ‘modern slavery hotspot’ in northern India to reduce the prevalence of bonded labour in the states of Uttar Pradesh and Bihar. Research was undertaken in this programme between 2014 and 2018 by IDS and Praxis Institute teams in both states.Freedom Fun

A Theory of Exploitative Child Labor

Child labor laws should aim to protect children who work, instead of trying to remove children from work. In this paper, we identify an instance when the risk of exploitation lowers the expected bene…t of child labor to the child,and therefore suppresses child labor force participation. Targeted legal intervention that lowers or removes the risk of exploitation raises child participation in the labor market, child welfare, and overall societal welfare. Targeting on child labor more broadly may reduce child labor force participation, child welfare, and overall societal welfare. Our key assumptions for generating these results are that parents decide for each child based on their child's best interest, that parents face imperfect information about the risks their children confront upon entering the labor market, and that firms may choose to exploit this information imperfection by employing children under forced-labor-type conditions.child labor, exploitation

Participatory Statistics to Measure Prevalence in Bonded Labour Hotspots in Tamil Nadu: Findings of the Base- and Endline Study

This report documents the findings of the Institute of Development Studies’ (IDS) and its partner, ‘Praxis Institute for Participatory Practices’, programme of research, learning and evaluation of the Freedom Fund funded operational work in a ‘modern slavery hotspot’ in Tamil Nadu to reduce the prevalence of bonded labour in the states of Tamil Nadu. Research was undertaken in this programme between 2016 and 2019 by IDS and Praxis Institute teams.Freedom Fun

Participatory Statistics to Measure Prevalence in Bonded Labour Hotspots in Uttar Pradesh and Bihar: Report of Preliminary Findings of the Baseline Study

The Institute of Development Studies has been carrying out a programme of research, learning and evaluation in relation to the Freedom Fund ‘hotspot’ in northern India, a project that seeks to reduce bonded labour in the states of Uttar Pradesh and Bihar. The work for this baseline study builds upon scoping visits comprising interviews with NGOs, focus groups with community members, field observations, the participatory collection and analysis of 353 life stories to identify the most significant indicators of change, and the generation of a baseline of participatory statistics of 3466 households across 82 hamlets in locations covered by 14 NGOs. This will be followed by the rollout of a systemic action research programme which combines stakeholders analysing and developing solutions to their problems with follow-up participatory statistical analysis. We will conduct an end-line survey two years after the data collection for this study has been completed. The aim of the study was to estimate the prevalence of bonded labour in the selected intervention communities of the Freedom Fund hotspot in northern India. Prevalence data help mainly to understand the profile of families in bonded labour and any correlations with different variables. The analysis of life stories provided a better insight into the life situations of families in bonded labour and explored questions of why and how. With clear causal factors emerging from the life story analysis, the current prevalence study was able to focus on these important indicators. The team facilitated a discussion on the results at the end of the data collection process in each site. These discussions focused on the reasons for the differences in prevalence results using the tallied-up data to explore how gender, age and caste dynamics shape bonded labour, with most adults in bonded labour working inside the village; most boys in bondage working outside the village; and a group of families with all members in bonded labour working outside the village.Freedom Fun