Trinque problem: covering complete graphs by plane degree-bounded hypergraphs

Let \(K_n\) be a complete graph drawn on the plane with every vertex incident to the infinite face. For any integers i and d, we define the (i, d)-Trinque Number of \(K_n\), denoted by \({\mathcal {T}}^d_{i}(K_n)\), as the smallest integer k such that there is an edge-covering of \(K_n\) by k “plane” hypergraphs of degree at most d and size of edge bounded by i. We compute this number for graphs (that is \(i=2\)) and gives some bounds for general hypergraphs.     

A professionalization framework to understand the structuring of work

The notion of professionalization is widely used both by managers and researchers. This use questions the traditional definition of profession. This paper reviews a book published in 1988 – The System of Professions – written by a sociologist, A. Abbott. Though this book had a strong impact in the field of the sociology of professions, it has remained unknown by many researchers in management science. His pragmatic approach to the concepts of profession and professionalization helps achieve better understanding of work structuring and as a consequence can be useful to address issues such as human resources management, organizational control or even the management of information systems.     

Pathological Gamblers: Inpatients’ versus Outpatients’ Characteristics

Several researchers and clinicians have questioned the advantages and disadvantages of inpatient and outpatient treatment for people suffering from pathological gambling. This study compares the characteristics of pathological gamblers seeking inpatient and outpatient treatment. A total of 233 pathological gamblers (inpatients = 134, outpatients = 99) participated in the study. Results show that inpatients have more severe gambling problems than those receiving outpatient services. Similar results were obtained on most other related variables such as anxiety, depression, alcohol consumption, and comorbidity. These results are discussed in terms of the costs and benefits of these two treatment modalities.     

Perceptron versus automaton in the finitely repeated prisoner’s dilemma

We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable by a machine with a bound on its complexity. One player has to use a finite automaton while the other player has to use a finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are different and not ordered by set inclusion. Repeated game payoffs are evaluated according to the limit of means. The main result establishes that a cooperation at almost all stages of the game is an equilibrium outcome if the complexity of the machines the players may use is limited enough and if the length T of the repeated game is sufficiently large. This result persists when more than T states are allowed in the player’s automaton. We further consider a variant of the model in which the two players are restricted to choosing strategies which are implementable by perceptrons and prove that the players can cooperate at most of the stages provided that the complexity of their perceptrons is sufficiently reduced.     

Self-Exclusion Program: A Longitudinal Evaluation Study

Few self-exclusion programs have been evaluated and their long-term impact remains unknown. This study has two main goals: (1) to assess changes in gambling behaviour and gambling problems for self-excluded patrons, and (2) to follow self-excluded gamblers for a two-year period (during and after the self-exclusion period). Individuals who excluded themselves (N = 161 at the initial stage) participated in telephone interviews after signing the self-exclusion agreement and were followed at 6, 12, 18 and 24-months. Results show that according to the DSM-IV, 73.1% of the participants were pathological gamblers. The self-exclusion program has many positive effects. During the follow-ups, the urge to gamble was significantly reduced while the perception of control increased significantly for all participants. The intensity of negative consequences for gambling was significantly reduced for daily activities, social life, work, and mood. The DSM score was significantly reduced over time. This reduction also took place between the baseline and the 6-month follow-up. The clinical implications of the results are discussed in relation to the effectiveness of the program. Suggestions are provided in order to increase compliance of self-excluded patrons.     

Safe sets in graphs: Graph classes and structural parameters

A safe set of a graph \(G=(V,E)\) is a non-empty subset S of V such that for every component A of G[S] and every component B of \(G[V {\setminus } S]\), we have \(|A| \ge |B|\) whenever there exists an edge of G between A and B. In this paper, we show that a minimum safe set can be found in polynomial time for trees. We then further extend the result and present polynomial-time algorithms for graphs of bounded treewidth, and also for interval graphs. We also study the parameterized complexity. We show that the problem is fixed-parameter tractable when parameterized by the solution size. Furthermore, we show that this parameter lies between the tree-depth and the vertex cover number. We then conclude the paper by showing hardness for split graphs and planar graphs.