Alain Hertz

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A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they indu...

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Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learnin...

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We study the average number \(A(G)\) of colors in the non-equivalent colorings of a graph \(G\). We show some general properties of this graph invariant ...

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The Bell numbers count the number of different ways to partition a set of \(n\) elements while the graphical Bell numbers count the number of non-equivalen...

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Let \(G=(V,E)\) be a graph and let \(S\subseteq V\) be a subset of its vertices. If the subgraph of \(G\) induced by \(V\setminus S\) is acyclic, the...

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Given a set \(\mathcal{R}\) of m disjoint finite regions in the 2-dimensional plane, all regions having polygonal boundaries, and given a set `(\mathc...

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Les algorithmes de partitionnement de données aident à identifier des sous-groupes homogènes en ce sens que les données de chaque groupe partagent des caract...

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This article discusses the precedence-constrained class sequencing problem (PCCSP). In scheduling terms, this is a one-machine scheduling problem with preced...

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We consider three colouring problems which are variations of the basic vertex-colouring problem, and are motivated by applications from various domains. We g...

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Recommender systems make use of different sources of information for providing users with recommendations of items. Such systems are often based on collabor...

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The eccentric connectivity index of a connected graph \(G\) is the sum over all vertices \(v\) of the product \(d_G(v)e_G(v)\), where \(d_G(v)\) is ...

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Given a directed graph \(G=(V,A)\), capacity and cost functions on \(A\), a root \(r\), a subset \(T \subset V\) of terminals, and an integer \(k\)...

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A graceful difference labeling (gdl for short) of a directed graph \(G\) with vertex set \(V\) is a bijection `(f:V\rightarrow{1,\ldots,\vert V\vert}...

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The eccentricity of a vertex \(v\) in a graph \(G\) is the maximum distance between \(v\) and any other vertex of \(G\). The diameter of a graph `(...

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Most papers on digital advertising focus on the point of view of Internet companies such as Google and Microsoft, and were written by people working for thos...

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We consider the problems of determining the metric dimension and the minimum cardinality of doubly resolving sets in \(n\)-cubes. Most heuristics develope...

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Nous donnons des conditions nécessaires et suffisante pour l'existence d'un graphe simple, ou d'un graphe connexe simple, ayant des nombres donnés `(m_{ij}...

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This article discusses the problem of unloading a sequence of boxes from a single conveyor line with a minimum number of moves. The problem under study is ef...

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Le problème de la détermination du plus grand sous-graphe \(k\)-colorable (\(k\)-MCSP) consiste à colorer autant de sommets que possible avec au plus `...

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Étant donné un graphe \(G\) complet, orienté, avec des poids sur les sommets et les arcs, une \(k\)-coloration \(\theta\)-impropre de \(G\) est une...

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