A note on dominating cycles in 2-connected graphs

Let G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) n for all triples of independent vertices x, y, z. We prove that every longest cycle in G is a dominating cycle unless G is a spanning subgraph of a graph belonging to one of four easily specified classes of graphs

Qualitative Research on Youths’ Social Media Use: A review of the literature

In this article we explore how educational researchers report empirical qualitative research about young people’s social media use. We frame the overall study with an understanding that social media sites contribute to the production of neoliberal subjects, and we draw on Foucauldian discourse theories and the understanding that how researchers explain topics and concepts produces particular ways of thinking about the world while excluding others. Findings include that 1) there is an absence of attention to the structure and function of social media platforms; 2) adolescents are positioned in problematic, developmental ways, and 3) the over-representation of girls and young women in these studies contributes to the feminization of problems on social media. We conclude by calling for future research that can serve as a robust resource for exploring adolescents’ social media use in more productive, nuanced ways

Orbiting Geophysical Observatory Attitude Control Subsystem Design Survey. NASA/ERC Design Criteria Program, Guidance and Control

This design survey summarizes the history of the Orbiting Geophysical Observatories' (OGO) Attitude Control Subsystem (ACS) from the proposal phase through current flight experience. Problems encountered in design, fabrication, test, and on orbit are discussed. It is hoped that the experiences of the OGO program related here will aid future designers

Polynomial algorithms that prove an NP-hard hypothesis implies an NP-hard conclusion

A number of results in Hamiltonian graph theory are of the form $\mathcal{P}$$_{1}$ implies $\mathcal{P}$$_{2}$, where $\mathcal{P}$$_{1}$ is a property of graphs that is NP-hard and $\mathcal{P}$$_{2}$ is a cycle structure property of graphs that is also NP-hard. Such a theorem is the well-known Chv\'{a}tal-Erd\"{o}s Theorem, which states that every graph $G$ with $\alpha \leq \kappa$ is Hamiltonian. Here $\kappa$ is the vertex connectivity of $G$ and $\alpha$ is the cardinality of a largest set of independent vertices of $G$. In another paper Chv\'{a}tal points out that the proof of this result is in fact a polynomial time construction that either produces a Hamilton cycle or a set of more than $\kappa$ independent vertices. In this note we point out that other theorems in Hamiltonian graph theory have a similar character. In particular, we present a constructive proof of the well-known theorem of Jung for graphs on $16$ or more vertices.. \u

"Women made it a home": Representations of women in social studies

This article explores recently published P-12 social studies lesson plans that include women to examine how attending to women is “getting done” in the field and how the lessons represent women and women’s experiences. Using discourse analysis methodologies, the author demonstrates that women have been included as topics in ways that do not work toward disrupting problematic discourses about gender norms. Through their avoidance of issues of power and patriarchy, most of the lessons fall short of addressing gender inequity – in the past or the present – in a significant way. More critical attention to women and gender in lessons, as well as in other curricular spaces, are important steps toward harnessing social studies’ potential to engage students in the meaningful consideration of inequitable gender relations

Good Teaching? An Examination of Culturally Relevant Pedagogy as an Equity Practice

The adoption of educational policy measures to close the achievement gap, as well as the significant amount of scholarship dedicated to the subject, are just some of the indicators that reflect the tremendous concern in education about the academic performance of students of color. Within research aimed at promoting equitable practices in education, culturally relevant teaching has emerged as a good teaching strategy to improve achievement. Using genealogical methods to examine the ways in which culture has become relevant to classroom practice, the author argues that the perceived difference from white students that made it possible to conceive of children of color as culturally deficit in the 1960s is also invoked in more recent literature that promotes attending to culture as an equity strategy. The take-up of culturally relevant teaching as something that a teacher can “do,” instead of a critical stance that a teacher takes, is also examined and critiqued

Feminism, Neoliberalism, and Social Studies

The purpose of this article is to analyze the sparse presence of women in social studies education and to consider the possibility of a confluence of feminism and neoliberalism within the most widely distributed National Council for the Social Studies (NCSS) publication, Social Education. Using poststructural conceptions of discourse, the author applies second-wave feminist theory and Fraser’s (2009) work on neoliberalism as lenses to illuminate the limited attention to women and feminism in this text during the 1980s in order to better understand how women have been marginalized in social studies education and to consider the possibility that the feminist principles present in social studies were taken up in service of neoliberal forces

Obstacles to Addressing Race and Ethnicity in the Mathematics Education Literature

This Research Commentary builds on a 2-stage literature review to argue that there are 4 obstacles to making a sociopolitical turn in mathematics education that would allow researchers to talk about race and ethnicity in ways that take both identity and power seriously. The obstacles discussed are (a) the marginalization of discussions of race and ethnicity; (b) the reiteration of race and ethnicity as independent variables; (c) absence of race and ethnicity from mathematics education research; and (d) the minimizing of discussions of race and ethnicity, even within equity-oriented work