Homogeneous structures, bipartite graphs, and partial orders

同质结构、二部图和偏序

• 批准号: EP/D048249/1
• 负责人: John Truss
• 金额: $ 21.69万
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD048249%2F1
• 关键词: Homogeneous; structures; bipartite; graphs; partial

This project is principally in combinatorics, and most particularly in the study of graphs and digraphs. These are formed from a set (of 'points') and edges, where between any two points there may or may not be an edge. For digraphs, the direction along the edge is important, for graphs, not so. If a graph subdivides into two parts such that the only edges are between points in different parts, then it is said to be bipartite.We are interested here in sufficiently 'symmetric' structures, that is, roughly, those for which two finite subsets which look the same, meaning that they have the same size and arrangements of edges, still look the same from the perspective of the whole structure. Classifications of all the structures of various kinds (such as graphs, digraphs, orders) which are sufficiently symmetric have featured prominently in recent work on combinatorics and model theory, and this has helped to achieve a better understanding of these structures.The research will build on earlier work of the proposer and research students about partial orders, and the links between partial orders, bipartite graphs, and digraphs, form a central theme. Techniques derived from partial orders will be applied to the above programme, to derive classifications for 2-arc transitive bipartite graphs, and sufficiently symmetric digraphs.

该项目主要是组合学，特别是图和有向图的研究。它们由一组（“点”）和边形成，其中任意两点之间可能有也可能没有边。对于有向图，沿边缘的方向很重要，对于图则不然。如果一个图细分为两个部分，使得唯一的边位于不同部分的点之间，则该图被称为二分图。我们在这里对足够“对称”的结构感兴趣，也就是说，粗略地说，两个有限子集看起来相同，这意味着它们具有相同的大小和边的排列，从整个结构的角度来看仍然看起来相同。足够对称的各种结构（例如图、有向图、阶）的分类在最近的组合学和模型理论研究中占据了突出的地位，这有助于更好地理解这些结构。这项研究将建立在提案者和研究生关于偏序的早期工作的基础上，以及偏序、二分图和有向图之间的联系构成了一个中心主题。从偏序导出的技术将应用于上述程序，以导出 2 弧传递二部图和充分对称有向图的分类。

项目成果

Uncountable cofinalities of automorphism groups of linear and partial orders

线性和偏序自同构群的不可数共尾性

• DOI: 10.1007/s00012-010-0040-0
• 发表时间: 2010
• 期刊: Algebra universalis
• 影响因子: 0.6
• 作者: Droste M

Countable homogeneous coloured partial orders

可数同质彩色偏序

• DOI: 10.4064/dm455-0-1
• 发表时间: 2008
• 期刊: Dissertationes Mathematicae
• 影响因子: 1.8
• 作者: De Sousa S

Some constructions of highly arc-transitive digraphs

高弧传递有向图的一些构造

• DOI: 10.1007/s00493-011-2523-9
• 发表时间: 2011
• 期刊: Combinatorica
• 影响因子: 1.1
• 作者: Amato D

Set-homogeneous directed graphs

集合齐次有向图

• DOI: 10.1016/j.jctb.2011.08.002
• 发表时间: 2012
• 期刊: Journal of Combinatorial Theory, Series B
• 作者: Gray R

Crown-free highly arc-transitive digraphs

无冠高弧传递有向图

• DOI: 10.1515/form.2011.055
• 发表时间: 2012
• 期刊: Forum Mathematicum
• 影响因子: 0.8
• 作者: Amato D