Graphes planaires et présentations des groupes de tresses.
We give a necessary and sufficient condition for the existence of a tree of order with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius.
In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph...