Discipline: 
Mathematics
Status: 
Available
Level: 
PhD Project
Level: 
Masters Project

Decompositions of complete graphs and complete multipartite graphs into cycles, paths and trails have received a fair amount of attention recently.  Existence and properties of such graph decompositions, especially in the case of multipartite graphs, still need much further investigation. There are many open problems with regard to properties such as being gregarious or being resolvable.
Related open work on so-called trades in graphs expand this project considerably, and extend the possible applications.