Graph Theory

The main focus is on structural and algorithmic point of views. The team established expertise includes problems such as finding large cycles in a given graph, graph colorings, covering problems, and extremal graph theory. For example, some team members are particularly interested in Thomassen’s conjecture: Every 4-connected line graph is Hamiltonian. Finding sufficient and computationally tractable conditions for a graph to be Hamiltonian is of significant importance from both theoretical and algorithmic viewpoints as Hamiltonicity is an NP-hard problem.

Generalization of such problems has also been recently considered for edge- or vertex-colored graphs. For example, one may look for properly colored spanning trees in an edge- or a vertex-colored graph. Alternatively, one may look for a dominating set in a vertex colored graph having at least one vertex from each color. Beside their theoretical interest, these extensions have applications in areas including biocomputing and web problems.

Many of the questions we consider can be stated in terms of (integer) linear optimization that is an expertise of new members of the team with research interests focusing on the combinatorial, computational, and geometric aspects of linear optimization. In this regard the aim would be to investigate recent results illustrating the significant interconnection between the most computationally successful algorithms for linear optimization and its generalizations, and the geometric and combinatorial structure of the input. Ideally, the deeper theoretical understanding will ultimately lead to increasingly efficient algorithms. Most of our research collaborations involve French research groups including LaBRI, LIRMM, LIAFA, and LIMOS as well as research groups in Europe, North America, China, Japan, India and South America.

Caractérisation de réseaux égocentrés par l'énumération de leurs sous-graphes induits

-- Raphaël Charbey (GALAC, LRI)

Résumé : La science des réseaux regroupe des méthodes issues de différentes disciplines qui ont néanmoins souvent du mal à percer au delà de celles-ci. Très utilisée en biologie moléculaire, notamment dans le cadre de l'étude des interactions entre protéines, l'énumération de l'ensemble des sous-graphes induits, jusqu'à ...

Mariage stable auto-stabilisant et distribué

-- Marie Laveau (GALAC, LRI)

Summary: Le problème du mariage stable (Stable Marriage problem, SMP) est un problème classique proposé pour la première fois par Gale et Shapley. Issu de l'économie, le SMP a aussi été étudié intensivement en maths et en informatique et a de multiples dérivés et applications (Cloud-computing, programme d'admission ...

Cycles dans les produits cartésiens de graphes

-- Evelyne Flandrin (GALAC, LRI)

Résumé : Les cycles dans les graphes ont été largement étudiés : cycles hamiltoniens, cycles de toutes les longueurs, cycles contenant des sommets ou des arêtes donnés, .... Nous passons en revue quelques-uns des résultats essentiels du domaines avant de nous intéresser à l'existence de cycles dans les produits cartésiens de graphes ...

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Translations: fr