Écoulement d'un fluide de Bingham dans un domaine non-cylindrique

We obtain an existence theorem for Bingham flows in a noncylindrical domain, as a simple application of a previous result on Bingham flows with a monotone perturbation.     

Le nombre minimal de colorations d'un hypergraphe k-chromatique

A (0,λ)-graph (λ?2) is a connected graph in which any two vertices have λ common neighbours or none at all. Such a graph is regular. When the diameter is at least four, a lower bound for the degree can be obtained. This lower bound is attained only by Hadamard graphs and n-cubes.     

Une condition suffisante d'existence d'un circuit hamiltonien dans un graphe oriente

In this article we prove that a sufficient condition for an oriented strongly connected graph with n vertices to be Hamiltonian is: (1) for any two nonadjacent vertices x and y

$\text{d}{}^{\mathrm{+}}\text{(x)+d}{}^{\mathrm{?}}\text{(x)+d}{}^{\mathrm{+}}\text{(y)+d}{}^{\mathrm{?}}\text{(y)?sn?1}$

.     

Écoulement d'un fluide de Bingham dans un domaine non-cylindrique avec singularité

We consider a Bingham flow on a noncylindrical domain with a singularity at t = 0. Using the well known technique of Galerkin approximations, we give an existence theorem. For the bidimensional case we also show uniqueness of the solution of our problem.     

Une relation de séparation entre cocircuits d'un matroide

Let S₁′S₂′S₃′ be 3 distinct cocircuits of a matroid M on a set E. We say that S₁′ does not separate S₂′ and S₃′ when S₂′\S₁′ and S₃′\S₁′ are included in one single and the same component of the submatroid M × (E\S₁′). Our main result is: A matroid is graphic if and only if from any 3 cocircuits having a non-empty intersection there is at least one which separates the two others.     

La reduction minimale d'un graphe a une reunion de cliques

On obtient la valeur maximale de l'indice de réduction minimale d'un graphe á une réunion de k cliques.     

Un probleme de partition de l'ensemble des parties a trois elements d'un ensemble fini

Let X be a set of n elements. Let $\text{T}$₃(X) be the set of all triples of X. We define a clique as a set of triples which intersect pairwise in two elements. In this paper we prove that if n?6, the minimum cardinality of a partition of $\text{T}$₃(X) into cliques is $\text{[}\text{1}\text{4}\text{(n?1)}{}^2\text{]}$.     

Nombre chromatique total d'un hypergraphe

In this paper, the author defines a hypergraph total chromatic number and determines this number for the complete h-partite and for the complete h-uniform hypergraphs.     

Arbres minimaux d'un graphe preordonne

We study the minimal spanning trees of a connected graph G = (X,U) where U is partially preordered (or quasi-ordered). We characterize several kinds of optimal spanning trees and give conditions for existence of strongly optimal trees. Generalizations to bases of matroids (binary matroïds in part 2) are immediate. Sone of our results are given in terms of Krugdahl's dependence graphs. They imply previous results of Rosenstiehl and Gale in the case of linear orders or preorders.     

Partitions lineaires arguesiennes d'un espace vectoriel

In this work, we study linear and desarguesian partitions of a finite dimensional vector space over a skew-field K. When K is finite, we describe the set of all these partitions as a homogeneous space of the general linear group and we give an enumeration formula.     

Polytope des independants d'un graphe serie-parallele

A graph is said to be serie-parallel if it doesn't contain an homeomorph to K₄. The aim of the paper is the demonstration of Chvatal's conjecture on the polytope of independent set of vertices in such graphs. This is done classically by using LP-duality, the algorithm for constructing the primal-dual solution having the nice property to be linear in the number of vertices.     

Les 5-colorations d'un graphe planaire forment une classe de commutation unique

There is one class of interchanges for the 5-colorations of a planer graph. As a consequence it is always possible to reach a four coloration (if it exists) by a sequence of interchange from any 5-coloration. A theorem is given for surfaces of genus g.