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

该奖项支持西弗吉尼亚大学张存权教授在图论方面的研究。张博士打算从图的圈覆盖、局部连通性和哈密尔顿连通性以及最长圈及其弦的三个角度继续他对图中的路和圈的研究计划。图论的起源可以追溯到两百年前，但主要是在最近半个世纪，该领域才成为一个活跃、肥沃和蓬勃发展的数学分支。图是连接点(点)的线(边)的网络，因此图的语言成为描述分离实体之间相互关系的自然方式。不仅在通信理论中大量使用图论，而且令人惊讶的是，在纯数学和应用数学的许多部分，以及理论计算机科学中都有图论的使用。

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.