Mathematical Sciences: Cycles and Paths in Graphs---Researchin Graph Theory

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This award supports the research in graph theory of Professor Cun-Quan Zhang of West Virginia University. Dr. Zhang intends to continue his program of research on the topic of paths and cycles in graphs, from the threefold point of view of cycle coverings of graphs, local connectivity and Hamiltonian connectivity, and the question of longest cycles and their chords. The beginnings of graph theory go back perhaps two hundred years, but it is mostly in the last half-century that the field has become an active, fertile, and flourishing branch of mathematics. A graph is a network of lines ("edges") joining points ("vertices"), so that the language of graphs becomes a natural way of describing interrelationships among separated entities. The uses of graph theory abound not only in communications theory but in surprisingly many parts of mathematics, both pure and applied, as well as theoretical computer science.