Edge lifting and total domination in graphs

Let u and v be vertices of a graph G, such that the distance between u and v is two and x is a common neighbor of u and v. We define the edge lift of uv off x as the process of removing edges ux and vx while adding the edge uv to G. In this paper, we investigate the effect that edge lifting has on the total domination number of a graph. Among other results, we show that there are no trees for which every possible edge lift decreases the total domination number and that there are no trees for which every possible edge lift leaves the total domination number unchanged. Trees for which every possible edge lift increases the total domination number are characterized.     

The internal migration patterns of the foreign-born and native-born populations in the United States: 1975-80 and 1985-90

"The focus of this article is on an examination of the influence of birthplace on the internal migration and spatial redistribution patterns of the foreign-born and native-born populations in the United States during the 1975-80 and 1985-90 periods. The analyses presented here consider the following principal questions: (1) What are the internal migration patterns of the foreign-born population in the United States, and how do they differ from those of the native-born population? (2) How do the relocation choices of various birthplace-specific foreign-born and native-born subpopulations differ from each other? (3) Are the internal migration patterns generating an increased or a decreased geographical concentration of such birthplace-specific subgroups?"     

School enrolment and mothers’ labor supply: evidence from a regression discontinuity approach

We analyze the impact on maternal employment of a universal school reform in Norway which lowered the school starting age from seven to six. We use a regression discontinuity approach exploiting exogenous variation in the compulsory school enrollment rule caused by the reform. Our results reveal positive short-term effects on labor supply (approximately five percentage points) and on earnings (about 12600/1350 NOK/Euro). Subgroup analyses show that the positive effects are much stronger for mothers with low wage potential, a group of mothers that were less likely to use formal childcare prior to the reform. The positive effects for this subgroup of mothers suggest that expanding child-care can be an effective tool for increasing labor supply of mothers who previously had relatively low labor market earnings potential.     

Graphs with large paired-domination number

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (1998) Networks 32: 199–206. A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by , is the minimum cardinality of a paired-dominating set of G. Let G be a connected graph of order n with minimum degree at least two. Haynes and Slater (1998) Networks 32: 199–206, showed that if n ≥ 6, then . In this paper, we show that there are exactly ten graphs that achieve equality in this bound. For n ≥ 14, we show that and we characterize the (infinite family of) graphs that achieve equality in this bound.Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.     

A parameterized perspective on packing paths of length two

We study (vertex-disjoint) packings of paths of length two (i.e., of P ₂’s) in graphs under a parameterized perspective. Starting from a maximal P ₂-packing ℘ of size j we use extremal combinatorial arguments for determining how many vertices of ℘ appear in some P ₂-packing of size (j+1) (if such a packing exists). We prove that one can ‘reuse’ 2.5j vertices. We also show that this bound is asymptotically sharp. Based on a WIN-WIN approach, we build an algorithm which decides, given a graph, if a P ₂-packing of size at least k exists in time O^*(2.448^3k)\mathcal{O}^{*}(2.448^{3k}) .     

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.