Mathematical Sciences: Circuit Covers and Integer Flows - Research in Graph Theory

该奖项支持张教授在组合学方面的研究工作。研究者将继续在电路覆盖、电路分解、整数流和图的边着色等主题上进行研究。本课题的主要目标是电路双盖猜想和整数流问题，以及一些相关的问题，包括一些图族的3边着色问题。这项研究是在组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散集合。离散系统的行为对现代通信极为重要。例如，大型网络的设计，如电话系统，以及计算机科学中算法的设计都涉及离散对象，这就利用了组合研究。

This award supports the research of Professor Zhang to work in combinatorics. The investigator will continue his investigations in the topics of circuit covers, circuit decompositions, integer flows, and edge-colorings of graphs. The major targets in this project will be the circuit double cover conjecture and integer flow problems together with some related problems, including the question of 3-edge-coloring for some families of graphs. The research is in the general area of combinatorics.Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.