An investigation of combinatorial problems

在图（网络）中搜索入侵者是我将要研究的问题之一。 我将考虑某些图表族，以期确定所需的最低搜索人数，或确定固定数量的可用搜索者所需的最短时间。研究的另一个主题是图分解。 这是我多年来一直在做的工作的延续。 一些结果在调度中有应用。最后一个广泛的研究课题是凯莱图。 这些图是用群构造的。 它们具有大量的对称性，这使得它们在一些令人惊讶的应用中非常有用。 我将主要从子图和同构的角度来研究它们。

Searching for intruders in graphs (networks) is one of the problems I shall be studying.  I shall be considering certain families of graphs with a view towards determining the minimum number of searchers required, or the minimum time required for a fixed number of available searchers. Another topic of investigation is graph decompositions.  This is a continuation of work I have been doing for many years.  Some of the results have applications in scheduling. The final broad topic of investigation is Cayley graphs.  These are graphs that are constructed using groups.  They possess a large amount of symmetry which makes them useful in some surprising applications.  I'll be looking at them mainly from the subgraph point of view and isomorphism point of view.