Fractional decomposition of graphs and the Nash-Williams conjecture (ARC Discovery Project externally administered by Monash University) (2024–2028)
Abstract:
Nash-Williams' conjecture is a famous unsolved problem about decomposing graphs (abstract networks).
Breakthrough results achieved in recent years have shown that the conjecture, along with other major graph
decomposition problems, could be solved if only more were known about fractional decomposition. This project
aims to clear this bottleneck to progress by dramatically expanding the state of knowledge on fractional
decomposition. Expected outcomes include major progress on Nash-Williams' conjecture and related graph decomposition problems. This should enhance Australia's research reputation in pure mathematics and provide benefits in downstream applications areas including statistics, data transmission, and fibre-optic networks.