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Skeletons in multigraphs

Václav Havel, Josef Klouda (1993)

Commentationes Mathematicae Universitatis Carolinae

Under a multigraph it is meant in this paper a general incidence structure with finitely many points and blocks such that there are at least two blocks through any point and also at least two points on any block. Using submultigraphs with saturated points there are defined generating point sets, point bases and point skeletons. The main result is that the complement to any basis (skeleton) is a skeleton (basis).

Sublattices of certain Coxeter lattices

Anne-Marie Bergé, Jacques Martinet (2005)

Journal de Théorie des Nombres de Bordeaux

In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.

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