Edge precoloring extension of hypercubes

We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most d − 1 edges of the d‐dimensional hypercube Qd can be extended to a proper d‐edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d‐edge colorings of Qd.Originally included in thesis in manuscript form. </p

Prevalence of problematic cell phone use in an adult population in Spain as assessed by the Mobile Phone Problem Use Scale (MPPUS)

Problematic cell phone use has alarmingly increased in industrialized countries in the past 10 years. For many perpetrators, it can turn into a behavioural addiction, although this is not a recognized medical condition. Although there are many tools for evaluating this use, one of the most widely used tools is the Mobile Phone Problematic Use Scale (MPPUS), which we test on a representative sample of the population in Spain to obtain an estimate of the prevalence of problematic cell phone use in our midst. The age range consists of 16-65 years, with 1,126 surveys conducted. In this population, we verify that the reliability and internal consistency of the MPPUS (α = 0.939) are maintained. Additionally, the construct validity, considering the derived factors (Abuse and Dependence, Craving and Loss of Control, and Dependence on the Social Environment) are aligned with other research and with diverse external criteria of addiction. We establish four categories of users (Casual, Regular, At Risk, and Problematic) and obtain a prevalence of 15.4% among At Risk Users and 5.1% among Problematic Users. This finding implies a total of 20.5% of Users with Problems. A binary logistic regression analysis shows that age, gender, level of education, and daily cell phone use predict problematic cell phone use. The results, based on multiple criteria, show that such problematic use shares features of recognized addictions, affecting large segments of the population and not only adolescents