Alain Hertz

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We consider the set of graphs that can be constructed from a one-vertex graph by repeatedly adding a clique or a stable set linked to all or none of the vert...

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Tactical wireless networks are used in cases where standard telecommunication networks are unavailable or unusable, e.g. disaster relief operations. We fully...

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Recommender systems provide personalized recommendations to their users for items and services. They do that using a model that is tailored to each user to i...

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The Twelfth Montreal IPSW took place on August 22-26, 2022, and was jointly organized by the Centre de recherches mathématiques (CRM) and the Institute for D...

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Recommender systems provide recommendations to their users for items and services by creating a model tailored to each user to infer their preferences based ...

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We investigate the ratio \(\mathcal{I}(G)\) of the average size of a maximal matching to the size of a maximum matching in a graph G. If many maximal mat...

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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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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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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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Clustering algorithms help identify homogeneous subgroups from data. In some cases, additional information about the relationship among some subsets of the d...

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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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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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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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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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