Randomly perturbed graphs: Problems between random and extremal graph theory
随机扰动图:随机图论与极值图论之间的问题
基本信息
- 批准号:422062814
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Fellowships
- 财政年份:2019
- 资助国家:德国
- 起止时间:2018-12-31 至 2020-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In mathematics, the exchange of ideas and methods between different areas often provides interesting new insights and leads to progress in the field. This project is located in discrete mathematics connecting random and extremal graph theory. Random graph theory is concerned with the analysis and properties of typical large graphs. In extremal graph theory rare rigid events forced by specific constraints and maximisation are studied extensively. In between these two, there is the model of randomly perturbed graphs, which is the union of a sparse random and a dense deterministic graph. This fascinating interplay of chaos and order features very interesting phenomena and contributes to our understanding of the behaviour of discrete structures. The focus of this project is on problems in this newly emerged model, which is currently attracting a lot of attention. There is a wide range of possibilities for interpolation between the purely random and the purely deterministic setup, which provides room for new challenging conjectures. Most of the questions ask for embeddings of spanning structures, such as Hamilton cycles, factors of graphs, trees, or general bounded degree graphs. These problems can be approached using a combination of methods from both areas with additional new techniques tailored towards the environment. Ultimately, advances in this perturbed model also promise progress in open questions in the pure setups.
在数学中,不同领域之间的思想和方法交流往往会提供有趣的新见解,并导致该领域的进步。该项目位于连接随机和极值图论的离散数学中。随机图理论主要研究典型大型图的分析和性质。在极值图论中,被特定约束和最大化所强迫的稀有刚性事件被广泛地研究。在这两者之间,有一个随机扰动图模型,它是一个稀疏随机图和一个稠密确定图的并集。这种令人着迷的混沌和秩序的相互作用呈现出非常有趣的现象,有助于我们理解离散结构的行为。这个项目的重点是这一新出现的模式中的问题,这一模式目前备受关注。在纯随机和纯确定性设置之间存在广泛的内插可能性,这为新的具有挑战性的猜想提供了空间。大多数问题都要求嵌入生成结构,如哈密尔顿圈、图的因子、树或一般有界度图。这些问题可以使用这两个领域的方法和针对环境量身定做的其他新技术的组合来解决。归根结底,这种扰动模型的进步也预示着在纯粹的设置中,公开问题也会取得进展。
项目成果
期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Anti-Ramsey threshold of cycles
反拉姆齐周期阈值
- DOI:10.1016/j.dam.2021.10.021
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:G. F. Barros;B. P. Cavalar;G. O. Mota;O. Parczyk
- 通讯作者:O. Parczyk
The size-Ramsey number of 3-uniform tight paths
- DOI:10.19086/aic.24581
- 发表时间:2019-07
- 期刊:
- 影响因子:0
- 作者:Jie Han;Y. Kohayakawa;Shoham Letzter;G. Mota;Olaf Parczyk
- 通讯作者:Jie Han;Y. Kohayakawa;Shoham Letzter;G. Mota;Olaf Parczyk
Maker-Breaker Games on Randomly Perturbed Graphs
随机扰动图上的 Maker-Breaker 博弈
- DOI:10.1137/20m1385044
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:D. Clemens;F. Hamann;Y. Mogge;O. Parczyk
- 通讯作者:O. Parczyk
Random Perturbation of Sparse Graphs
稀疏图的随机扰动
- DOI:10.37236/9510
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:M. Hahn-Klimroth;G. S. Maesaka;Y. Mogge;S. Mohr;O. Parczyk
- 通讯作者:O. Parczyk
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Dr. Olaf Parczyk其他文献
Dr. Olaf Parczyk的其他文献
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