Smart infrastructure (telecommunications, public transport, smart cities)
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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...
BibTeX referenceVariable Neighborhood Search for Extremal Graphs. 23. On the Randic Index and the Chromatic Number
Let <img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple graph with vertex degrees <img src="/cgi-bin/mimetex.cgi?d1, d2, \ldots, d_n...
BibTeX referenceComparing the Zagreb Indices
Let <img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple graph with <img src="/cgi-bin/mimetex.cgi?n=|V|"> vertices and <img src="/cgi-bin/...
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Given a simple connected graph <i>G = (V,E)</i> the geodetic closure <i>I [S]</i> <img src="/cgi-bin/mimetex.cgi?\subset"> <i>V</i> of a subset <i>S</i...
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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...
BibTeX referenceVariable Neighborhood Search for Extremal Graphs. 18. Conjectures and Results about the Randic Index
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...
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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...
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In the integrated aircraft routing, crew scheduling and flight retiming problem, a minimum-cost set of aircraft routes and crew pairings must be constructed...
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In this paper, we study the problem of determining the capacity requirements for applications that require QoS guarantees. We consider three kinds of source ...
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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...
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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...
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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...
BibTeX referenceOn a Conjecture About the Randic Index
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...
BibTeX referenceSet covering and packing formulations of graph coloring: algorithms and first polyhedral results
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...
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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...
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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...
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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...
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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 ...
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The variable neighborhood search metaheuristic is applied to the primal simple plant location problem and to a reduced dual obtained by exploiting the compl...
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We consider vehicle routing and crew scheduling problems that involve a lexico- graphic bi-level objective function (for instance, minimizing first the numb...
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