The Edge-Connectivity of Vertex-Transitive Hypergraphs

A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex-transitive hypergraph is maximally edge-connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex-transitive hypergraphs which are not maximally edge-connected.Comment: 8 page

Existential Closure in Line Graphs

A graph $G$ is $n$-existentially closed if, for all disjoint sets of vertices $A$ and $B$ with $|A\cup B|=n$, there is a vertex $z$ not in $A\cup B$ adjacent to each vertex of $A$ and to no vertex of $B$. In this paper, we investigate $n$-existentially closed line graphs. In particular, we present necessary conditions for the existence of such graphs as well as constructions for finding infinite families of such graphs. We also prove that there are exactly two $2$-existentially closed planar line graphs. We then consider the existential closure of the line graphs of hypergraphs and present constructions for $2$-existentially closed line graphs of hypergraphs.Comment: 13 pages, 2 figure

Distance-Restricted Firefighting on Finite Graphs

In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph $G$ and then $b$ firefighters protect $b$ vertices. On each subsequent turn, the fire spreads to the collective unburnt neighbourhood of all the burning vertices and the firefighters again protect $b$ vertices. Once a vertex has been burnt or protected it remains that way for the rest of the game. We previously introduced the concept of $\textit{distance-restricted firefighting}$ where the firefighters' movement is restricted so they can only move up to some fixed distance $d$ and they may or may not be permitted to move through burning vertices. In this paper we establish the NP-Completeness of the distance-restricted versions of the $\textit{Maximum Vertices Saved}$ problem and present an integer program for solving these problems. In the penultimate section we also discuss some interesting properties of the $\textit{Expected Damage}$ function

Enhanced skills in global health and health equity: Guidelines for curriculum development

Introduction: Global health addresses health inequities in the care of underserved populations, both domestic and international. Given that health systems with a strong primary care foundation are the most equitable, effective and efficient, family medicine is uniquely positioned to engage in global health. However, there are no nationally recognized standards in Canada for postgraduate family medicine training in global health.Objective: To generate consensus on the essential components of a Global Health/Health Equity Enhanced Skills Program in family medicine.Methods: A panel comprised of 34 experts in global health education and practice completed three rounds of a Delphi small group process.Results: Consensus (defined as ≥ 75% agreement) was achieved on program length (12 months), inclusion of both domestic and international components, importance of mentorship, methods of learner assessment (in-training evaluation report, portfolio), four program objectives (advocacy, sustainability, social justice, and an inclusive view of global health), importance of core content, and six specific core topics (social determinants of health, principles and ethics of health equity/global health, cultural humility and competency, pre and post-departure training, health systems, policy, and advocacy for change, and community engagement).Conclusion: Panellists agreed on a number of program components forming the initial foundation for an evidence-informed, competency-based Global Health/Health Equity Enhanced Skills Program in family medicine

The Firebreak Problem

Suppose we have a network that is represented by a graph $G$. Potentially a fire (or other type of contagion) might erupt at some vertex of $G$. We are able to respond to this outbreak by establishing a firebreak at $k$ other vertices of $G$, so that the fire cannot pass through these fortified vertices. The question that now arises is which $k$ vertices will result in the greatest number of vertices being saved from the fire, assuming that the fire will spread to every vertex that is not fully behind the $k$ vertices of the firebreak. This is the essence of the {\sc Firebreak} decision problem, which is the focus of this paper. We establish that the problem is intractable on the class of split graphs as well as on the class of bipartite graphs, but can be solved in linear time when restricted to graphs having constant-bounded treewidth, or in polynomial time when restricted to intersection graphs. We also consider some closely related problems

Surf and turf: predation by egg-eating snakes has led to the evolution of parental care in a terrestrial lizard

Animals display a great diversity of parental care tactics that ultimately enhance offspring survival, but how such behaviors evolve remains unknown for most systems. Here, we studied the evolution of maternal care, in the form of nest guarding, in a single population of long-tailed sun skink (Eutropis longicaudata) living on Orchid Island (Taiwan). This species typically does not provide protection to its offspring. Using a common garden experiment, we show that maternal care is genetically determined in this population. Through field manipulations, we demonstrate that care provides a significant increase in egg survival on Orchid Island by reducing predation from egg-eating snakes (Oligodon formosanus); this predator is not abundant in other populations of the lizard, which do not display parental care. Finally, using extensive field surveys, we show that the seasonal availability of green sea turtle (Chelonia mydas) nests is the cause for the high abundance of snake predators on Orchid Island, with the snakes consuming lizard eggs when green turtle eggs are not available. Together, these lines of evidence provide the first full demonstration of how predation can trigger the evolution of parental care in a species derived from a non-caring ancestor

Status of global health fellowship training in the United States and Canada

Background: Increasing numbers of residency graduates desire global health (GH) fellowship training. However, the full extent of training options is not clear. Objective: To identify clinical GH fellowships in all specialties in the U.S. and Canada and to describe their demographics, innovative features, and challenges. Methods: The authors surveyed program directors or designees from GH fellowships with a web-based tool in 2017. Program directors reported demographics and program characteristics. Results: The authors identified 85 potential programs. Fifty-four programs (63.5%) responded confirming 50 fellowships. The number of U.S. GH fellowship programs increased by 89.7% since 2010. One-third of fellowships accepted graduates from more than one specialty. The most common single-specialty programs were Emergency Medicine or Family Medicine. Fellowship duration was most commonly 24 months. Median size was one fellow per year. Funding and lack of qualified applicants were significant challenges. Most programs were funded through fellow billing for patient care or other means of self-support.   Conclusions: The number of U.S. and Canadian GH fellowship programs has nearly doubled since 2010. Programs reported lack of funding and qualified applicants as their most significant challenges. Consensus amongst stakeholders regarding training requirements may improve outcomes for future fellows, their employers, and the patients they serve

An Investigation of Cancer Rates in the Argentia Region, Newfoundland and Labrador: An Ecological Study

Background. The Argentia region of Newfoundland and Labrador, Canada, was home to a US naval base during a 40-year period between the 1940s and the 1990s. Activities on the base resulted in contamination of the soil and groundwater in the region with chemicals such as heavy metals and dioxins, and residents have expressed concern about higher rates of cancer in their community. This study investigated the rate of cancer diagnosis that is disproportionately high in the Argentia region. Methods. Cases of cancer diagnosed between 1985 and 2011 were obtained for the Argentia region, two comparison communities, and the province of Newfoundland and Labrador. Crude and age-standardized incidence rates of cancer diagnosis were calculated and compared. The crude incidence rate was adjusted for differences in age demographics using census data, and age-standardized incidence rates were compared. Results. Although the Argentia region had a higher crude rate of cancer diagnosis, the age-standardized incidence rate did not differ significantly from the comparison communities or the provincial average. Argentia has an aging population, which may have influenced the perception of increased cancer diagnosis in the community. Conclusions. We did not detect an increased burden of cancer in the Argentia region