Gilles Caporossi

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Cahiers du GERAD

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A graph invariant is a function of a graph <i>G</i> which does not depend on labeling of <i>G</i>’s vertices or edges. An algebraic expression of one or sev...

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The multidimensional scaling (MDS) aims at finding coordinates for a set of <i>n</i> objects in a (low) <i>q</i> dimensional space that best fits dissimilar...

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We consider the problem of separating two sets of points in an Euclidean space with a hyperplane that minimizes the sum of <i>L<sub>p</sub></i>-norm distanc...

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

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

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

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In this paper, we present tools to help understanding the dynamics of cognitive processes involved in handwriting and in text composition. Three computer sy...

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Conjectures in graph theory have multiple forms and involve graph invariants, graph classes, subgraphs, minors and other concepts in premisses and/or conclu...

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Let <i>G</i> be a simple graph on <i>n</i> vertices with the eigenvalues (of an adjacency matrix) &lambda;<sub>1</sub> &ge; &lambda;<sub>2</sub> &ge; ... &g...

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

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

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

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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...

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Graffiti's conjecture 105 states that for any tree the range of transmissions of distance is greater than or equal to the range of degrees. After using the ...

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On the basis of a variable-neighbourhood search with the AutoGraphiX software, it is conjectured that for even numbers of atoms the fully conjugated acycli...

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The distance matrix of a chemical graph can be computed in quadratic time, and from it can be obtained the distance level patterns (DLP), Wiener, Szeged and...

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In the set of bicolored trees with given numbers of black and of white vertices we describe those for which the largest eigenvalue is extremal (maximal or m...

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Fusenes are simply connected, geometrically planar or non-planar polyhexes. Enumeration of such systems with up to 20 hexagons, <i>i.e.,</i> a set 4000 tim...

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The definition of a fullerene as a cubic polyhedron made up entirely of pentagons and hexagons is compatible with a huge variety of isomeric forms for struc...

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By means of the variable neighborhood search algorithm, a newly designed heuristic approach to combinatorial optimization, we established the structure of t...

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