A graph G with a list of colors L(v) and weight w(v) for each vertex v is (L,w)-colorable if one can choose a subset of w(v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets. In this paper, we give necessary and sufficient conditions for a weighted path to be (L,w)-colorable for some list assignments L. Furthermore, we solve the problem of the free-cho...

A graph G is said to be F-residual if for every point u in G, the graph obtained by removing the closed neighborhood of u from G is isomorphic to F. Similarly, if the remove of m consecutive closed neighborhoods yields Kn, then G is called m-Kn-residual graph. Erdös determine the minimum order of the m-Kn-residual graph for all m and n, the minimum order of the connected Kn-residual graph is fo...

An econometric model is specified in which an individual’s income and the income mix of the neighbourhood in which the individual resides are endogenous, thus providing a holistic model of phenomena that previously have been fragmented into neighbourhood effects and neighbourhood selection literatures. To overcome the biases from selection and endogeneity, the parameters of this model are estim...

STUDY OBJECTIVE To provide reliability information for a brief observational measure of physical disorder and determine its relation with neighbourhood level crime and health variables after controlling for census based measures of concentrated poverty and minority concentration. DESIGN Psychometric analysis of block observation data comprising a brief measure of neighbourhood physical disord...

Study objective: Using a conceptual rather than a mathematical approach, this article proposed a link between multilevel regression analysis (MLRA) and social epidemiological concepts. It has been previously explained that the concept of clustering of individual health status within neighbourhoods is useful for operationalising contextual phenomena in social epidemiology. It has been shown that...

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

BACKGROUND Recent increases in violent crime may impact a variety of health outcomes in Mexico. We examined relationships between neighbourhood-level violence and smoking behaviours in a cohort of Mexican smokers from 2011 to 2012, and whether neighbourhood-level social cohesion modified these relationships. METHODS Data were analysed from adult smokers and recent ex-smokers who participated ...

OBJECTIVE To assess the relationship between socioeconomic deprivation and health-related quality of life in urban neighbourhoods, using a multilevel approach. METHODS Of the population-based cohort EPIPorto, 1154 georeferenced participants completed the 36-Item Short-Form Health Survey. Neighbourhood socioeconomic deprivation classes were estimated using latent-class analysis. Multilevel mod...