Embedding spanning subgraphs into dense graphs via the regularity method

通过正则性方法将跨越子图嵌入到稠密图中

• 批准号: 43496149
• 负责人: Professor Dr. Anusch Taraz
• 金额: --
• 依托单位: Lehrstuhl für Diskrete Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/43496149?language=en
• 关键词: Embedding; spanning; subgraphs; into; dense

The main theme of this research project is to determine essentially best-possible sufficient conditions for the embedding of large substructures into dense graphs. Building on the results and methods we obtained and developed for the proof of the Bollobäs-Komlös conjecture and problems in its vicinity during the first funding period of this project, we are now aiming for a variety of other central embedding problems in extremal combinatorics. Our key machinery will again be the regularity method, but it is clear that progress towards these goals will require substantial new ideas in order to cope with subgraphs of unbounded maximum degree and arbitrary order, sparse host graphs, median degree conditions or packings of exhaustive families of trees. In this way the overall aim of the project is to make progress on a set of important open problems and conjectures while simultaneously advancing the methodology.

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项目成果

An Extension of the Blow-up Lemma to Arrangeable Graphs

爆炸引理对可排列图的扩展

• DOI: 10.1137/13093827x
• 期刊: SIAM J. Discret. Math.
• 作者: J. Böttcher;Y. Kohayakawa;A. Taraz;A. Würfl
• 通讯作者: A. Würfl

Spanning embeddings of arrangeable graphs with sublinear bandwidth

具有次线性带宽的可排列图的跨越嵌入

• DOI: 10.1002/rsa.20593
• 发表时间: 2015
• 期刊: Random Structures & Algorithms
• 影响因子: 1
• 作者: J. Böttcher;A. Taraz;A. Würfl
• 通讯作者: A. Würfl

The Approximate Loebl-Komlós-Sós Conjecture I: The Sparse Decomposition

近似 Loebl-Komlós-Sós 猜想 I：稀疏分解

• DOI: 10.1137/140982842
• 期刊: SIAM J. Discret. Math.
• 作者: J. Hladký;J. Komlós;D. Piguet;M. Simonovits;M. Stein;E. Szemerédi
• 通讯作者: E. Szemerédi

An approximate version of the tree packing conjecture

树包装猜想的近似版本

• DOI: 10.1007/s11856-015-1277-2
• 发表时间: 2016
• 期刊: Israel Journal of Mathematics
• 影响因子: 1
• 作者: Böttcher J

Almost Spanning Subgraphs of Random Graphs After Adversarial Edge Removal

对抗性边缘去除后几乎跨越随机图的子图

• DOI: 10.1017/s0963548313000199
• 发表时间: 2013
• 期刊: Combinatorics, Probability and Computing
• 作者: J. Böttcher;Y. Kohayakawa;A. Taraz
• 通讯作者: A. Taraz