Graphs and Hypergraphs

图和超图

• 批准号: 170450-2013
• 负责人: Brown, Jason
• 金额: $ 1.38万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=522812
• 关键词: Graphs; Hypergraphs

The first part of the project concentrates on answering a variety of graph theoretical questions via connections to other branches of mathematics. First, using analytic, algebraic and combinatorial techniques, I will investigate problems related to the roots of such polynomials in terms of the the largest modulus, real and imaginary parts among graphs of order n. As well, new generalizations of colouring polynomials have arisen that take into account forbidden sets of colours at the vertex sets, and some difficult extremal problems require more attention. Connections have suggested that a deeper exploration of the algebras over finite fields as a way to further bound the polynomials and locate their roots. Also, I plan to investigate whether a famous open problem on the colouring number of a certain product of two graphs might yield to a matrix-theoretic approach.

该项目的第一部分集中于通过与其他数学分支的联系来回答各种图论问题。首先，使用解析、代数和组合技术，我将根据n阶图中的最大模、实部和虚部来研究与这些多项式的根相关的问题。此外，已经出现了新的着色多项式的推广，考虑了顶点集上的禁止颜色集，并且一些困难的极值问题需要更多的关注。连接表明，在有限域上对代数进行更深入的探索，作为进一步约束多项式和定位其根的一种方式。此外，我计划研究一个著名的开放问题，关于两个图的某个积的着色数是否可以产生矩阵论的方法。