Consider a convex polygon <i>V_n</i> with <i>n</i> sides, perimeter <i>P_n</i>, diameter <i>D_n</i>, area <i>A_n</i>,...

Quel octogone de diamère unité (ou petit octogone) possède la plus grande surface ou le plus grand périmètre? Serait-ce l'octogone régulier? Eh! non, il n'en...

A conjecture of Delorme, Favaron and Rautenbach [DM 257 (2002) 29-38] about the Randic index of a graph, in relation to its order and minimum degree, is ref...

<p>Le système <i>AutoGraphiX (AGX1 et AGX2)</i> permet, parmi d’autres fonctions, la génération automatique de conjectures en théorie des graphes. Nous étud...

<p>Using the <i>AutoGraphiX 2</i> system, a systematic study is made on generation and proof of relations of the form</p> <center> $\underline{b}_n \leq ...

We consider two (0,1)-linear programming formulations of the graph (vertex-) coloring problem, in which variables are associated to stable sets of the input...

<i>L</i>₁ norm discrimination consists in finding the hyperplane that minimizes the sum of <i>L</i>₁ norm distances between the hyperp...

The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasonin...

A survey is made of the AutoGraphiX (AGX) research program for computer as- sisted and, for some functions, automated graph theory.

Usual graph classes, such as complete graphs, paths, cycles and stars, frequently appear as extremal graphs in graph theory problems. Here we want to turn t...

The <i>p</i>-median problem is one of the basic models in discrete location theory. As with most location problems, it is classified as NP-hard, and so, heu...

The variable neighborhood search metaheuristic is applied to the primal simple plant location problem and to a reduced dual obtained by exploiting the compl...

This paper examines the plant location problem under the objective of maximizing return-on-investment. However, in place of the standard assumption that all...

Several upper bounds on the largest Laplacian eigenvalue of a graph <i>G</i>, in terms of degree and average degree of neighbors of its vertices, have been ...

The AutoGraphiX (AGX) system for computer assisted or, for some of its functions, fully automated graph theory was developed at GERAD, Montreal since 1997. ...

The continuous location-allocation problem requires finding sites for <i>m</i> new facilities in the plane in order to serve <i>n</i> users such that the to...

Variable Neighborhood Search (VNS) is a recent and effective metaheuristic for solving combinatorial and global optimization problems. It is capable of esca...

Les problèmes de chargement statique de groupes turbo-alternateurs à vapeur peuvent être exprimés sous forme de minimisation d’une somme de fonction de coût ...

Dynamic programming is applied to the economic dispatch problem with spin- ning reserve constraint. A first algorithm, based on a direct application of Bell...

The global <i>k</i>-means heuristic is a recently proposed (Likas et al. 2003) incremental approach for minimum sum-of-squares clustering of a set <i>X</i> ...