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.

Nash-Williams猜想是关于图(抽象网络)分解的一个著名的悬而未决的问题。近年来取得的突破性结果表明，只要对分数分解有更多的了解，这个猜想和其他主要的图分解问题就可以得到解决。这个项目旨在通过极大地扩展关于分数分解的知识状态来消除这一瓶颈。预期结果包括纳什-威廉姆斯猜想和相关的图形分解问题的主要进展。这将提高澳大利亚在纯数学领域的研究声誉，并在包括统计、数据传输和光纤网络在内的下游应用领域提供好处。