Mathematical Sciences: Contractible Edges, Cycle Covers, andApplications

余教授将研究图论的两个领域。他将研究可收缩边及其应用，以及循环、循环覆盖和循环分解。图论始于200多年前欧拉的工作，但直到最近半个世纪，这个领域才开始蓬勃发展。它现在是数学中最活跃、最丰富的分支之一。图是由线（“边”）连接点（“顶点”）组成的网络，因此图论成为研究分离实体之间相互关系的自然工具。图论不仅用于通信理论，而且令人惊讶地用于纯数学和应用数学的许多部分，以及理论计算机科学。

Professor Yu will work in two areas of graph theory. He will study contractible edges and their applications, as well as cycles, cycle covers, and cycle decompositions. Graph Theory began more than two hundred years ago with the work of L. Euler, but it is only in the last half-century that the field has flourished. It is now one of the most active, fertile branches of mathematics. A graph is a network of lines ("edges") joining points ("vertices"), so that graph theory becomes a natural tool for studying interrelationships among separated entities. Graph Theory is used not only in Communications Theory but in surprisingly many parts of pure and applied mathematics, as well as in Theoretical Computer Science.