The notion of the line hypergraph is introduced. It is an immediate generalization of two wellknown objects: a line graph and a dual hypergraph. We obtain various characterizations of line hypergraphs; we also obtain a generalization of Whitney's theorem. The NP-completeness of the problem of determining whether a given graph is the line graph of a hypergraph of rank r > 2 is proved.
Discrete Mathematics and Applications provides the latest information on the development of discrete mathematics in Russia to a world-wide readership. The journal covers various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.