Category: seminars
On the intervals of framing lattices
summary: A flow graph G is an acyclic oriented graph with \(V(G) = [n]\), \(E(G)\) a multi-set of edges where each edge \((i,j)\) satisfies \(i<j\), and such that \(G\) has a unique source \(s=1\) and sink \(t=n\). On such a graph, a route is simply ...
On the Structure of Potential Counterexamples to the Borodin-Kostochka Conjecture
summary: The Borodin-Kostochka conjecture, a long-standing problem in graph theory, asserts that every graph \(G\) with maximum degree \(\Delta \geq 9\) satisfies \(\chi(G) \leq max \{\Delta - 1, \omega(G)\}\) where \(\chi(G)\) and \(\omega(G)\) are respectively the chromatic number and the clique number of \(G\). While the conjecture ...
Excluding a rectangular grid
summary: For every positive integer k, we define the k-treedepth as the largest graph parameter td_k satisfying (i) td_k(∅)=0; (ii) td_k(G) <= 1+ td_k(G-u) for every graph G and every vertex u; and (iii) if G is a (
Computability of Compact Spaces
summary: The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres, closed manifolds and finite graphs without endpoints : if a set X is homeomorphic to a sphere, a closed manifold or such a graph, then any ...
Classes de sous-shifts définis par des formules logiques.
summary: Une configuration est un coloriage du plan Z². Habituellement, les ensembles de configurations étudiés sont ceux définis par un ensemble de motifs "interdits" n'apparaissant dans aucune des configurations de l'ensemble. De tels ensembles sont appelés sous-shifts. Dans ce séminaire, on définit les ensembles de configurations grâce à ...
Manytamaris: on descriptions of the Tamari lattice
summary: Manytamaris is a website about the Tamari lattice. The interest in this particular lattice stems from its many properties, besides being a lattice, and its numerous appearances in different areas of mathematics. As such, the goal for Manytamaris is to be a survey on the descriptions of the Tamari ...
Algorithms for Stochastic Analysis Using SageMath
summary: This talk explores algorithms for computations in stochastic analysis and their increasing relevance in modern mathematics. We present algorithms to explicitly solve Stochastic Differential Equations via Itô's Lemma, and derive solutions of certain partial differential equations using Feynman–Kac formula. Hence, emphasizing the need for developing SageMath packages ...
Eliminating more than vertices in graphs
summary: Considérons le jeu suivant sur un graphe. À chaque tour, le joueur peut enlever un sommet de chaque composante connexe du graphe courant. Le but du jeu est d’éliminer tous les sommets du graphe. Le nombre minimum de tours nécessaires est appelé la treedepth du graphe. C’est ...
Reconstruction de graphes via des requêtes sur les triplets
summary: Considérons un oracle disposant d'un graphe labellisé caché. L'objectif de la reconstruction de graphes est de retrouver ce graphe caché en interrogeant l'oracle avec certains types de requêtes. Les requêtes que nous examinons portent sur des triplets de sommets du graphe, plus précisément, sur la structure ...
Fractional domatic number and minimum degree
summary: We present a study of a graph parameter in graph theory, named the fractional domatic number. A dominating set in a graph is a set of vertices such that every vertex outside the set is adjacent to a vertex in the set. The domatic number of a graph is ...
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