Fractional decomposition of graphs and the Nash-Williams conjecture

图的分数式分解和纳什-威廉姆斯猜想

• 批准号: DP240101048
• 负责人: A/Prof Daniel Horsley
• 金额: $ 29.2万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-01-01 至 2027-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240101048
• 关键词: Fractional; decomposition; graphs; Nash; Williams

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.

纳什·威廉姆斯（Nash-Williams）的猜想是分解图（抽象网络）的著名未解决的问题。近年来取得的突破性结果表明，如果只有更多关于分数分解的知识，就可以解决该猜想以及其他主要的图分解问题。该项目旨在通过大大扩展分数分解的知识状态来清除这种瓶颈的进展。预期的结果包括纳什·威廉姆斯（Nash-Williams）的猜想和相关图分解问题的重大进展。这应该提高澳大利亚在纯数学方面的研究声誉，并为下游应用领域提供好处，包括统计，数据传输和光纤网络。