We define two classes of lower bounds using either one or two simplices for the minimization of a concave function over a polytope. For each of them, a pro...

Consider <i>N</i> entities to be classified (e.g., geographical areas), a matrix of dissimilarity between pairs of entities, a graph <i>H</i> with vertices a...

It is well known that the set of correlated equilibrium distributions of a noncooperative game is a convex polytope that includes all the Nash equilibrium ...

We explore how a simple linear change of variable affects the inclusion functions obtained with Interval Analysis methods. Univariate and multivariate pol...

We present an exact algorithm and three applications of nonconvex quadratically constrained quadratic programming. First, we consider the pooling problem fro...

We develop and analyze parallelization strategies for the Variable Neighborhood Search (VNS) meta-heuristic applied to the <i>p</i>-median problem. The stra...

Albertson (1997) defines the <i>imbalance</i> of an edge (<i>i,j</i>) in <i>E</i> of a graph <i>G</i> = (<i>V,E</i>) as | <i>d_i - d_j</...

This paper studies the duality gap in the simple plant location problem, and presents general formulas for the gap when certain complementary slackness cond...

After a short historic review, we briefly describe a new algorithm for constructive enumeration of polyhex and fusene hydrocarbons. In this process our alg...

Generalized logical analysis aims at modelling complex biological systems, especially the so-called regulatory systems like genetic networks. The main feat...

Recently, Araujo and De la Pena (1998) gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramifi...

The pooling problem, which is fundamental to the petroleum industry, describes a situation where products possessing different attribute qualities are mixed...

We prove that amongst all fullerenes the dodecahedron has maximum smallest eigenvalue (equal to -<img src="G0234-1.gif" align=middle>), followed by the thre...

The AutoGraphiX (AGX) system determines classes of extremal or near extremal graphs with a Variable Neighborhood Search heuristic. From these, conjectures m...

A survey is made of computer systems which help to obtain and sometimes provide automatically proofs, conjectures and refutations in graph theory.

We study various uniform <i>k</i>-partition problems which consist in partitioning <i>m</i> sets, each of cardinality <i>k</i>, into <i>k</i> sets of cardin...

Let <i>G</i> be a graph and <i>d_v</i> the degree (= number of first neighbors) of its vertex <i>v</i>. The connectivity index of <i>G</i> is <img...

We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.

In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non is...

A generalization of the Roy-Gallai theorem on the chromatic number of a graph is derived which is also an extension of several other results of Berge and of...