The Hamilton-Waterloo Problem with even cycle lengths

The Hamilton-Waterloo Problem HWP$(v;m,n;\alpha,\beta)$ asks for a 2-factorization of the complete graph $K_v$ or $K_v-I$, the complete graph with the edges of a 1-factor removed, into $\alpha$ $C_m$-factors and $\beta$ $C_n$-factors, where $3 \leq m < n$. In the case that $m$ and $n$ are both even, the problem has been solved except possibly when $1 \in \{\alpha,\beta\}$ or when $\alpha$ and $\beta$ are both odd, in which case necessarily $v \equiv 2 \pmod{4}$. In this paper, we develop a new construction that creates factorizations with larger cycles from existing factorizations under certain conditions. This construction enables us to show that there is a solution to HWP$(v;2m,2n;\alpha,\beta)$ for odd $\alpha$ and $\beta$ whenever the obvious necessary conditions hold, except possibly if $\beta=1$; $\beta=3$ and $\gcd(m,n)=1$; $\alpha=1$; or $v=2mn/\gcd(m,n)$. This result almost completely settles the existence problem for even cycles, other than the possible exceptions noted above

Barriers to the Employment of Welfare Recipients

Dramatic reductions in welfare caseloads since passage of the Personal Responsibility and WorkOpportunity Reconciliation Act of 1996 have not allayed policy concerns about the employability of recipients remaining on the rolls. Analysis of potential barriers to employment can address whether current recipients have problems that either singly or in combination make it difficult for them to comply with the new requirements for getting and keeping jobs. In this paper, we explore the prevalence and work effects of 14 potential barriers in a new survey of a representative sample of 753 urban single-mother recipients. We report the prevalence of the barriers and how their number predicts employment rates, controlling for demographic characteristics. We also analyze which individual barriers are associated with employment and how a model inclusive of a comprehensive array of barriers improves upon a traditional human capital model of the work effects of education and work and welfare history. Single mothers who received welfare in 1997 had higher rates of personal health and mental health problems, domestic violence, and children’s health problems than do women in national samples, but they were no more likely than the general population to be drug or alcohol dependent. Only 15 percent of respondents had none of the barriers and almost two-thirds had two or more barriers. The numbers of multiple barriers were strongly and negatively associated with working, and among the individual barriers, low education, lack of access to transportation, poor health, having drug dependence or a major depressive disorder, and several experiences of workplace discrimination reduced employment. Welfare-to-work programs need to be more finely targeted with respect to exemptions and service provision, and states should consider providing longer-term and enhanced supports for those who face low prospects of leaving welfare for employment.

A Comprehensive Approach to Truancy for Baltimore City: A Roundtable Discussion

The University of Baltimore School of Law Center for Families, Children and the Courts (CFCC), one of three centers of excellence within the School of Law, is a national leader in promoting family justice system reform. CFCC’s mission is to create, foster and support local, state, and national movements to integrate communities, families, and the justice system in order to improve the lives of families and the health of the community. CFCC’s Truancy Court Program (TCP), created in 2004, exemplifies these goals through the operation of a court-school-CFCC partnership that leverages the stature, authority, and expertise of each of these three entities to tackle the truancy crisis in Baltimore City. Beginning with five Baltimore City public elementary and middle schools, the TCP has since expanded to six elementary/middle schools and one high school. The model is based on an early intervention, therapeutic, and non-adversarial approach to truancy. It targets students who are “soft” truants – students who have from three to twenty unexcused absences – in the belief that this group still has academic, social, and emotional connections to the school. The judge or master volunteers his/her time to collaborate each week with the TCP team. In addition to the judge or master, the team consists of school representatives, a CFCC staff person, a University of Baltimore law student, the TCP Mentor, the TCP School Liaison, the child, and his/her parent/caregiver. While the TCP saw immediate and dramatic improvement in school attendance, behavior and performance among participating TCP students, CFCC quickly recognized that there were few, if any, other interventions to address truancy. Until recently, Baltimore City schools relied almost exclusively on the TCP to provide an approach to truant behavior. At the same time, public attention focused increasingly on the extraordinarily high number of unexcused absences in Baltimore’s public schools. While chronic truancy was rampant throughout the state, it was far and away more pervasive in Baltimore City than in any of the counties