Subgraph extension problem: structures, characterizations and its connection with edge-weighting coloring problems

子图扩展问题：结构、表征及其与边加权着色问题的联系

• 批准号: RGPIN-2014-05317
• 负责人: Yu, Qinglin
• 金额: $ 0.8万
• 依托单位: Thompson Rivers University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=611567
• 关键词: Subgraph; extension; problem; structures; characterizations

Subgraph extension and graph coloring problems Graph Theory is an old but re-born and energized branch of mathematics. It has grown rapidly since the 1960’s with its applications spreading to Physics, Biology and Operations Research, in particular to Computing Science and communication networks. Often graphs are used as a working frame for various scientific investigations. In particular, Computing Science has provided many interesting problems for Graph Theory to grow. More recently, Graph Theory has become a useful instrument for the study of gene sequences, environment sustainability, management science and logic designing. The proposed program is to expand our knowledge on graph factors, subgraph extension and its connection to other combinatorial topics. The objectives are to acquire knowledge, both for research and HQP training in three ways: 1) To understand the structures of subgraph extension graphs (i.e., (Y, H)-extendable graphs) by developing a decomposition procedure for the purpose of general recursive arguments. Such a decomposition will be vital for the design of efficient algorithms to recognize and to construct the family of such graphs. This work involves to generalize the existing techniques and methods, and to create new analysis tools for the general framework and abstract models. 2) The research will deliver a more consistent and universal framework for the potential applications of subgraph extension to other combinatorial problems and other mathematical branches. The concept, (Y, H)-extendable graphs, is a well-defined framework, which not only consolidate many well-known concepts (e.g., factor-critical graph, bicritical graphs and defect-d matching) together and also maintain the basic properties of its sub-classes. This enables us to simplify many of the previous proofs and establish closer connections to other graph theory problems. 3) In our proposal, we have stated many closely related and well-defined problems. These problems have different levels of difficulties, from conjectures and open problems, to generalization of known results and construction of specified classes of graphs; we also carefully select and blend the problems in proposal by considering our short-term and long-term objectives. The problems proposed will fulfill my vision in the study of subgraph extension and also provide opportunities for involvement of undergraduate and graduate students to engage in creation, exploration and experiencing rigorous research.

子图扩展和图形问题 图形是一种古老的，但自1960年的应用程序向物理学，生物学和操作研究，尤其是计算机科学和通信网络的应用程序科学有问题的问题，即将成为理论，基因的研究，环境可持续性，管理科学和逻辑。 拟议的计划是扩大我们与其他组合主题的联系。 1）通过为一般递归参数的它们的e开发一个分解过程，了解该子图扩展图的结构（即（y，h） - 扩展图）。识别和构建此类图的家族。 2）该研究将为其他组合LEM和其他数学分支的潜在应用提供更普遍的框架。众所周知的概念（例如，关键因素图和缺陷D匹配）在一起，还保持其子类的支撑物。 3）在我们的提案中，我们有密切相关且定义明确的问题。术语和目标。提出的问题将在pH扩展研究中的愿景，还为劳动和毕业生提供了贡献的态度。