We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have be...

Let &nbsp;<img src="/cgi-bin/mimetex.cgi?G=(V,E)">&nbsp; be a simple graph with vertex degrees &nbsp;<img src="/cgi-bin/mimetex.cgi?d1, d2, \ldots, d_n...

Let &nbsp;<img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple graph with &nbsp;<img src="/cgi-bin/mimetex.cgi?n=|V|"> vertices and &nbsp;<img src="/cgi-bin/...

Given a simple connected graph <i>G = (V,E)</i> the geodetic closure <i>I&nbsp;[S]</i> <img src="/cgi-bin/mimetex.cgi?\subset"> <i>V</i> of a subset <i>S</i...

The AutoGraphiX research program led to a new type of application of metaheuristics in graph theory, <i>i.e.</i>, finding conjectures on graph invariants by...

Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form <img src="/cgi-bin/mimetex.cgi?lbn \leq R \oplus i \leq ub...

Colour image quantization is a data compression technique that reduces the total set of colours in an image to a representative subset. This problem is expr...

In the integrated aircraft routing, crew scheduling and flight retiming problem, a minimum-cost set of aircraft routes and crew pairings must be constructed...

In this paper, we study the problem of determining the capacity requirements for applications that require QoS guarantees. We consider three kinds of source ...

Given buses of different types arriving at a depot during the evening, the bus parking problem consists of assigning these buses to parking slots in such a w...

We consider the problem of locating a circle with respect to existing facilities on the plane, such that the largest weighted distance between the circle and...

In this article we consider the problem of assigning parking slots to buses of different types so that the required buses can be dispatched easily in the mo...

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...

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...

In a transit authority bus depot, buses of different types arrive in the evening to be parked in the depot for the night, and then dispatched in the morning...

We consider a widespread solution method that consists of a column generation approach embedded in a branch-and-bound scheme to solve the multiple depot veh...

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...

We consider a crew scheduling problem with preferential bidding in the airline industry. We propose a new methodology based on a graph coloring model and a ...

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

We consider vehicle routing and crew scheduling problems that involve a lexico- graphic bi-level objective function (for instance, minimizing first the numb...