Graph coloring with cardinality constraints on the neighborhoods

AbstractExtensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V1,…,Vk of the vertex set of G such that, for some specified neighborhood Ñ(v) of each vertex v, the number of vertices in Ñ(v)∩Vi is (at most) a given integer hvi. The complexity of some variations is discussed according to Ñ(v), which may be the usual neighbors, or the vertices at distance at most 2, or the closed neighborhood of v (v and its neighbors). Polynomially solvable cases are exhibited (in particular when G is a special tree)

A discrete model for studying existence and uniqueness of solutions in nonlinear resistive circuits

AbstractTwo combinatorial problems raised by the fundamental question of the existence and uniqueness of solutions in nonlinear electric circuits are presented. The first problem, namely the existence of a pair of conjugate trees, has been solved in polynomial time using an original model based on matroïd intersection. For the second problem, which is the search of a particular orientation in a multigraph with labeled edges, an elaborate branch and bound procedure is proposed

Comparing league formats with respect to match importance in Belgian football

Recently, most clubs in the highest Belgian football division have become convinced that the format of their league should be changed. Moreover, the TV station that broadcasts the league is pleading for a more attractive competition. However, the clubs have not been able to agree on a new league format, mainly because they have conflicting interests. In this paper, we compare the current league format, and three other formats that have been considered by the Royal Belgian Football Association. We simulate the course of each of these league formats, based on historical match results. We assume that the attractiveness of a format is determined by the importance of its games; our importance measure for a game is based on the number of teams for which this game can be decisive to reach a given goal. Furthermore, we provide an overview of how each league format aligns with the expectations and interests of each type of club

Solving the Sports League Scheduling Problem with Tabu Search

In this paper we present a tabu approach for a version of the Sports League Scheduling Problem. The approach adopted is based on a formulation of the problem as a Constraint Satisfaction Problem (CSP). Tests were carried out on problem instances of up to 40 teams representing 780 integer variables with 780 values per variable. Experimental results show that this approach outperforms some existing methods and is one of the most promising methods for solving problems of this type

The critical view of safety during laparoscopic cholecystectomy: Strasberg Yes or No? An Italian Multicentre study

Background: Laparoscopic cholecystectomy is considered the gold standard for the treatment of gallbladder lithiasis; nevertheless, the incidence of bile duct injuries (BDI) is still high (0.3–0.8%) compared to open cholecystectomy (0.2%). In 1995, Strasberg introduced the "Critical View of Safety" (CVS) to reduce the risk of BDI. Despite its widespread use, the scientific evidence supporting this technique to prevent BDI is controversial. Methods: Between March 2017 and March 2019, the data of patients submitted to laparoscopic cholecystectomy in 30 Italian surgical departments were collected on a national database. A survey was submitted to all members of Italian Digestive Pathology Society to obtain data on the preoperative workup, the surgical and postoperative management of patients and to judge, at the end of the procedure, if the isolation of the elements was performed according to the CVS. In the case of a declared critical view, iconographic documentation was obtained, finally reviewed by an external auditor. Results: Data from 604 patients were analysed. The study population was divided into two groups according to the evidence (Group A; n = 11) or absence (Group B; N = 593) of BDI and perioperative bleeding. The non-use of CVS was found in 54.6% of procedures in the Group A, and 25.8% in the Group B, and evaluating the operator-related variables the execution of CVS was associated with a significantly lower incidence of BDI and intraoperative bleeding. Conclusions: The CVS confirmed to be the safest technique to recognize the elements of the Calot triangle and, if correctly performed, it significantly impacted on preventing intraoperative complications. Additional educational programs on the correct application of CVS in clinical practice would be desirable to avoid extreme conditions that may require additional procedures