Which trees have a differentiating-paired dominating set?

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998), 199–206). A paired-dominating set of a graph G with no isolated vertex is a dominating set S of vertices whose induced subgraph has a perfect matching. The set S is called a differentiating-paired dominating set if for every pair of distinct vertices u and v in V(G), N[u]∩S≠N[v]∩S, where N[u] denotes the set consisting of u and all vertices adjacent to u. In this paper, we provide a constructive characterization of trees that do not have a differentiating-paired dominating set.     

Analyzing the Effect of Express Orders on Supply Chain Costs and Delivery Times

Delivery time differentiation is a supply chain concept that has been implemented in various industries, but not yet in the automotive industry. One reason is that the effects of delivery time differentiation on the supply chain are not well understood. The BMW Group, for instance, has considered offering an express order option, where express orders bypass standard orders in the supply chain processes to achieve short delivery times. Express orders distort planning processes, increase operations cost, and increase the delivery times of standard orders, however the effects have not been quantified yet. This study analyzes the impact of express orders on the supply chain, when express orders are built‐to‐order. To understand the supply chain consequences of express orders better, we analyzed the relevant supply chain processes at BMW Group. We determine the effect that built‐to‐order express orders have on delivery times and on component demand. To analyze the effect of introducing express orders on expected delivery times and expected cost, we use queuing theory and derive expressions for the transient behavior of a discrete time batch queue. Our analyses indicate that many supply chain processes are only marginally affected. However, the orders to the suppliers become considerably more uncertain, which must be compensated by additional safety stock. Our results indicate that express orders can be an attractive option for BMW and other automotive companies. If the fraction of express orders stays at a reasonable level, express orders can be delivered within about two weeks.     

Vernetzte Zusammenarbeit erfolgreich gestalten – eine Analyse der Relevanz sozialer Fertigkeiten der Mitglieder in Gesundheitsnetzwerken

Due to recent strategic network building among health care partners a more differentiated discussion about the crucial structural and the personal success factors for network building and cooperation is needed. On that note, research has repeatedly emphasized the importance of the network agents’ individual soft skills. At the same time the empirical insights into this research topic are still scarce and the assumed interrelation between an agent’s individual repertoire of skills and his influence on the collaboration remain hypothetical so far. In the present paper we use the construct of so-called “political skills” to empirically test the impact of these skills on how they will contribute to the network members’ success within the cooperation. Using social network analysis the interaction structures between members in a doctors’ network (N = 37) are mapped and related to the individual level of political skills. It can be shown that primarily the dimension “networking ability” contributes to a beneficial role within the cooperation in terms of high prestige and high engagement as perceived by the other network members. In addition, members who scored high on that dimension are more likely to obtain benefits on an individual level (gaining new patients) as well as on a group level (identification with the network). One core implication that derives from the study’s results is the necessity to focus not only on strategic aspects with regard to building and designing health care networks, but also to develop and to foster personal soft-skills.     

Theoretische und statistische Modellierung von Cross-Pressures in Kontextanalysen

Cross-pressures can be defined as individually perceived social pressure that results from heterogeneity in the social context, mainly due to conflicting social expectations of relevant social actors. In this paper we discuss the theoretical position of “cross-pressures” in the structural-individualist paradigm and present methods for modeling cross-pressures in multilevel regression models. We argue that cross pressures form a specific class of context effects, that is macro-micro links, and sketch a reconstruction as part of the problem of defining the social situation in the Model of Frame Selection. The theoretical model implies that empirical applications of the concept would ideally use multiplicative terms for the specification of cross-level interactions in multilevel models. Modeling random slopes and context fixed-effects the interaction can be identified empirically. As an example we analyze the relation between postmaterialism and environmental concern, moderated by national wealth using WVS data. Our results indicate that postmaterialism and environmental concern form an integrated value cluster in wealthy societies, but are separate constructs in poorer societies.     

Modellvergleich und Ergebnisinterpretation in Logit- und Probit-Regressionen

In the social sciences logit and probit models are often used multivariate data analysis procedures for binary dependent variables. Both procedures can be thought of as resting on a linear model for an unobserved variable y* from which a nonlinear model for the probability of y?=?1 is derived. We first show that compared to linear models this nonlinearity leads to problems of interpreting results from such analysis. In particular odds ratios (exponentiated logit coefficients) often used in logistic regression are problematic in this respect. Instead we recommend using graphical procedures and reporting (corrected) average marginal effects (AME). Based on a series of Monte-Carlo simulations we next demonstrate that the regression coefficients from logit and probit models should not be compared between nested models. Because model building in the social sciences often employs a stepwise procedure a method allowing valid comparisons of effect sizes between models would be advantageous. Results from our simulation study show that average marginal effects and regression coefficients corrected by a method proposed by Karlson et al. (Sociological Methodology 42, 2012) lead to satisfactory results in many different scenarios. In contrast, y*-standardized coefficients are of limited utility and coefficients from a linear probability model should only be used with normally distributed variables.     

Perfect graphs involving semitotal and semipaired domination

Let G be a graph with vertex set V and no isolated vertices, and let S be a dominating set of V. The set S is a semitotal dominating set of G if every vertex in S is within distance 2 of another vertex of S. And, S is a semipaired dominating set of G if S can be partitioned into 2-element subsets such that the vertices in each 2-set are at most distance two apart. The semitotal domination number \(\gamma _\mathrm{t2}(G)\) is the minimum cardinality of a semitotal dominating set of G, and the semipaired domination number \(\gamma _\mathrm{pr2}(G)\) is the minimum cardinality of a semipaired dominating set of G. For a graph without isolated vertices, the domination number \(\gamma (G)\), the total domination \(\gamma _t(G)\), and the paired domination number \(\gamma _\mathrm{pr}(G)\) are related to the semitotal and semipaired domination numbers by the following inequalities: \(\gamma (G) \le \gamma _\mathrm{t2}(G) \le \gamma _t(G) \le \gamma _\mathrm{pr}(G)\) and \(\gamma (G) \le \gamma _\mathrm{t2}(G) \le \gamma _\mathrm{pr2}(G) \le \gamma _\mathrm{pr}(G) \le 2\gamma (G)\). Given two graph parameters \(\mu \) and \(\psi \) related by a simple inequality \(\mu (G) \le \psi (G)\) for every graph G having no isolated vertices, a graph is \((\mu ,\psi )\)-perfect if every induced subgraph H with no isolated vertices satisfies \(\mu (H) = \psi (H)\). Alvarado et al. (Discrete Math 338:1424–1431, 2015) consider classes of \((\mu ,\psi )\)-perfect graphs, where \(\mu \) and \(\psi \) are domination parameters including \(\gamma \), \(\gamma _t\) and \(\gamma _\mathrm{pr}\). We study classes of perfect graphs for the possible combinations of parameters in the inequalities when \(\gamma _\mathrm{t2}\) and \(\gamma _\mathrm{pr2}\) are included in the mix. Our results are characterizations of several such classes in terms of their minimal forbidden induced subgraphs.     

Leaving the Nordic Path? The Changing Role of Danish Trade Unions in the Welfare Reform Process

For a long period, Denmark has been labeled a ‘model country’ with a comprehensive welfare state and a successful model of corporatist policy‐making. Danish unions are considered amongst the strongest in the world, and they have for a long time been a distinct part of the political system, and as social partners, they were strongly integrated into decision‐making processes. The analysis of the Danish welfare and labour market policy during the last two decades documents a profound change in the arrangement and in the status of the social partners (especially unions) in the Danish political system. The results show that two important pillars of the Danish model – the social partner basis and the collective trust in partnership – are eroding. Unions are no longer part of the law‐making process and, since 2007, they are formally excluded from the organization of the decision‐making process. Recent developments point at weaker unions that operate more as lobbyists instead of being strong corporatist institutions or part of the decision‐making process. The results of the study are thought‐provoking and the basis for a revised thinking of the Danish and the Nordic model.     

A note on domination and total domination in prisms

Recently, Azarija et al. (Electron J Combin:1.19, 2017) considered the prism \(G \mathop {\square }K_2\) of a graph G and showed that \(\gamma _t(G \mathop {\square }K_2) = 2\gamma (G)\) if G is bipartite, where \(\gamma _t(G)\) and \(\gamma (G)\) are the total domination number and the domination number of G. In this note, we give a simple proof and observe that there are similar results for other pairs of parameters. We also answer a question from that paper and show that for all graphs \(\gamma _t(G \mathop {\square }K_2) \ge \frac{4}{3}\gamma (G)\), and this bound is tight.     

Elterliche Arbeitslosigkeitsdynamiken und Bildungsverläufe vom Ende der Grundschulzeit bis zum jungen Erwachsenenalter

In the present study, we examine the influence of parental unemployment on the educational outcomes of children in Germany. We consider the educational pathways from the transition to secondary school until early adulthood at age 23. In particular, we focus on the question whether children of unemployed parents are less likely to enroll in tertiary education. In addition, we look at enrolment into educational tracks at the beginning and the end of secondary school. We use data from the Socio-Economic Panel (SOEP). We address the problem of social selectivity into unemployment by means of a comprehensive control variable approach within the framework of random effects-models. In addition, we estimate fixed effects-models using siblings’ information. As a result, it is evident that a significant influence of unemployment on educational outcomes can be observed both with comprehensive control of status characteristics as well as in sibling models. However, this does not apply to all educational outcomes and not to all forms of unemployment.