Edge decomposition of dense graphs

This project aims to exploit and extend recently-developed breakthrough techniques in order to address fundamental open problems concerning edge decomposition of dense graphs, including a famous conjecture of Nash-Williams. Edge decomposition of graphs is a topic of vital concern in the mathematical fields of graph theory, combinatorial design theory, and finite geometry. It is of deep theoretical significance in these areas, and also has strong applications to digital communication and information technologies. It is anticipated that the project will result in powerful new methods for edge decomposition of dense graphs, the solution of famous open problems, and a deeper, more cohesive understanding of edge decomposition.