Spherical tilings by congruent quadrangles : forbidden cases and substructures

In this article we show the non-existence of a class of spherical tilings by congruent quadrangles. We also prove several forbidden substructures for spherical tilings by congruent quadrangles. These are results that will help to complete of the classification of spherical tilings by congruent quadrangles

Types of triangle in plane Hamiltonian triangulations and applications to domination and k-walks

We investigate the minimum number t(0)(G) of faces in a Hamiltonian triangulation G so that any Hamiltonian cycle C of G has at least t(0)(G) faces that do not contain an edge of C. We prove upper and lower bounds on the maximum of these numbers for all triangulations with a fixed number of facial triangles. Such triangles play an important role when Hamiltonian cycles in triangulations with 3-cuts are constructed from smaller Hamiltonian cycles of 4-connected subgraphs. We also present results linking the number of these triangles to the length of 3-walks in a class of triangulation and to the domination number

Construction of planar 4-connected triangulations

In this article we describe a recursive structure for the class of 4-connected triangulations or - equivalently - cyclically 4-connected plane cubic graphs

Gender and educational differences in the association between smoking and health-related quality of life in Belgium

Previous studies have shown that smoking has a significant and negative association with health-related quality of life (HRQOL). A question remains, however, as to whether this association between smoking and HRQOL differs by gender or educational level. To examine this question, we extracted data from the 2013 Belgian Health Interview Survey (n = 5668). HRQOL was assessed using the descriptive system of the EuroQol 5D-5L that consists of 5 dimensions and the resulting index score. Linear and logistic multivariable regression models were fitted to estimate the association between HRQOL and smoking for each educational level and gender. Also, interaction terms were introduced in the full regression models and the Wald test was used to assess model fit. Our findings show that among men, there is no significant association between smoking and HRQOL, and no effect modification by educational level. Among women, however, daily smokers have shown significantly lower HRQOL scores compared with never smokers, but only among females with a low and intermediate educational level. The lower EQ-5D index scores among female daily smokers with lower education was due to higher odds of reporting problems in anxiety/depression, mobility, pain, and usual activities. To conclude, information on the association between HRQOL and smoking is useful for the development of smoking cessation interventions. Our findings suggest the importance of tailoring these interventions to the needs of the women with lower education

Hamiltonian-connectedness of triangulations with few separating triangles

We prove that 3-connected plane triangulations containing a single edge contained in all separating triangles are hamiltonian-connected. As a direct corollary we have that 3-connected plane triangulations with at most one separating triangle are hamiltonian-connected. In order to show bounds on the strongest form of this theorem, we proved that for any s >= 4 there are 3-connected triangulation with s separating triangles that are not hamiltonian-connected. We also present computational results which show that all `small' 3-connected triangulations with at most 3 separating triangles are hamiltonian-connected