Abstract
Stimulated by its numerous applications, the theory of graphs continuously progresses in various domains. The concept of graph in itself varies in accordance with authors and problems considered: it belongs to the logic of sets as well as to combinatorial topology. Questions may be grouped into three main classes: the study of characteristic properties (invariants such as connectivity, existence of Hamiltonian circuits, Ramsey numbers); problems of embedding on surfaces (planarity, genus, thickness) and of graph-coloring; and enumeration of given classes of graphs, a peculiarly difficult field of investigation. Hypergraphs present a generalization of graphs from a set theoretic point of view. In spite of its rapid growth, graph theory has not yet reached its deep unity.
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