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.     

Caregiver drug use and arrest as correlates of child trauma exposure

This study proposed to determine the prevalence of substance use and drug-related arrests among caregivers of children referred to Child Protective Services (CPS), examine the relationship between substance use and arrests among caregivers, and examine the main effects and interaction of substance use and arrests in predicting child trauma exposure. Secondary data was collected from CPS files for a randomly selected group of 1127 children. Findings indicated that rates of caregiver substance misuse and arrests were higher than the general population, which was expected. When controlling for demographic and other variables, there was a main effect of substance use and arrests on child trauma exposure, but no significant interaction. Implications for caregivers engaged in substance use and/or involvement with the criminal justice system are discussed, as well as clinical and research implications for children exposed to trauma related to caregiver behaviors.     

The Impact of Historical Trauma and Mistrust on the Recruitment of Resource Families of Color

ABSTRACT

The Multiethnic Placement Act of 1994 and the Interethnic Adoption Provisions of 1996 (MEPA-IEP) require states to diligently recruit “potential foster and adoptive families that reflect the ethnic and racial diversity of children in the state for whom foster and adoptive homes are needed” (42 U.S.C. §622b(3)(9)). Nationally, 53% of the children in foster care and 55% of the children waiting to be adopted are children of color (Adoption and Foster Care Analysis and Reporting System, 2014). Recruitment of resource families of color has historically presented challenges. This article critically examines the diligent recruitment efforts of an urban county targeting Black/African American, Latino, and Native American communities through a critical race theory lens. Although there was an overall increase in resource families, the racial and ethnic representation of resource families to children in care within the county improved for Latinos yet declined for Black/African Americans and Native Americans. Theoretically, these results indicate that the historical mistrust of communities of color toward the child welfare system is a barrier to successful recruitment of resource families from these communities.     

MODELING THE ECONOMIC INTERACTION OF AGENTS WITH DIVERSE ABILITIES TO RECOGNIZE EQUILIBRIUM PATTERNS

We model differences among agents in their ability to recognize temporal patterns of prices. Using the concept of DeBruijn sequences in two dynamic models of markets, we demonstrate the existence of equilibria in which prices fluctuate in a pattern that is independent of the fundamentals and that can be recognized only by the more competent agents. (JEL: C7, D4, S477)     

Patterns of Information Source Use Across Industrial Purchase Situations*

An empirical taxonomy of industrial customers' information source use is developed based on a survey of 636 industrial customers across a wide range of different purchase situations. The taxonomy reveals five distinct information source mixes. Each mix consists of the combination of individual information sources used in a purchase situation. The five information source mixes are related to select underlying characteristics of purchase situations. The results indicate that the multivariate dimensions of purchase involvement, purchase complexity, and multiple influence are all significantly related to customers' choice of an information source mix. Implications of the taxonomy for marketing management and research are discussed.     

Factors Associated with Long-Term Survival of Family Businesses: Duration Analysis

This study identified factors influencing family business survival using National Family Business Panel and Spatial Hazard Events and Losses data. Sustainable Family Business Theory guided the use of a parametric duration model of long-term survival. Community characteristics, family achievements, family processes during change, business and owner characteristics, and business processes during stability affected long-term survival. Economic vulnerability of rural counties, family income from business, hiring temporary help, business size, viewing business as a way of life, and owner experience were associated with increased duration of business survival. Being home-based, a female owner, and customer-focused were associated with decreased duration of survival. Some family processes and achievements increased the duration of business survival; none decreased it.     

Reciprocal Relations across Time between Basic Values and Value‐expressive Behaviors: A Longitudinal Study among Children

The current study examines the reciprocal relations between children's values and value‐expressive behavior over a sixth‐month period. Three hundred and ten sixth‐grade students in Italy completed value and value‐expressive behavior questionnaires three times in three‐month intervals during the scholastic year. We assessed Schwartz's (1992) higher‐order values of conservation, openness to change, self‐enhancement, and self‐transcendence, as well as their respective expressive behaviors. Reciprocal relations over time between values and behaviors were examined using a cross‐lagged longitudinal design. Results showed that values and behaviors had reciprocal longitudinal effects on one another, after the stability of the variables was taken into account (i.e., values predicted change in behaviors, but also behaviors predicted change in values). Our findings also revealed that: (1) values were more stable over time than behaviors and (2) the longitudinal effect of values on behaviors tended to be stronger than the longitudinal effect of behaviors on values. Findings are discussed in light of the recent developmental literature on value change.