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Extremal Combinatorics

极值组合学

基本信息

批准号：
EP/K012045/1
负责人：
Oleg Pikhurko
金额：
$ 33.8万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FK012045%2F1
关键词：
Extremal Combinatorics

项目摘要

Extremal Combinatorics studies relations between various parameters of discrete structures. This area experienced a remarkable growth in the last few decades. Various aspects of Computer Science and Operations Research motivated by large-scale practical problems have been relying on more and more sophisticated combinatorial techniques and have posed a whole array of new challenging problems in Discrete Mathematics. At the same time, the development of powerful and deep mathematical methods has greatly expanded the horizon of combinatorial questions that can be approached now, meeting many of the above challenges. The project will concentrate on central questions of Extremal Combinatorics. Two examples are the the Turan function that asks how local restrictions can affect the global size of a hypergraph and the Ramsey theory that investigates whether large structures contain highly ordered substructures. These problems seem to be notoriously difficult and even some basic questions remain open. The previous attempts, although not completely successful, led to a number of useful techniques and insights. Some recent developments (such as hypergraph regularity, graph limits, and flag algebras) give us new powerful tools that may be instrumental in obtaining progress on these problems. The project aims at achieving a better understanding of these areas and developing generally useful methods and techniques.

极值组合学研究离散结构的各种参数之间的关系。该领域在过去几十年中经历了显着的增长。由大规模实际问题推动的计算机科学和运筹学的各个方面一直依赖于越来越复杂的组合技术，并在离散数学中提出了一系列新的具有挑战性的问题。与此同时，强大而深入的数学方法的发展极大地扩展了现在可以解决的组合问题的视野，满足了上述许多挑战。该项目将集中于极值组合学的核心问题。两个例子是图兰函数（询问局部限制如何影响超图的全局大小）和拉姆齐理论（研究大型结构是否包含高度有序的子结构）。这些问题似乎非常困难，甚至一些基本问题仍然悬而未决。之前的尝试虽然没有完全成功，但产生了许多有用的技术和见解。最近的一些发展（例如超图正则性、图极限和标志代数）为我们提供了新的强大工具，可能有助于在这些问题上取得进展。该项目旨在更好地了解这些领域并开发普遍有用的方法和技术。

项目成果

期刊论文数量（10）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

On Two Problems in Ramsey--Turán Theory

论拉姆齐的两个问题--图兰理论

DOI：
10.1137/16m1086078
发表时间：
2017
期刊：
SIAM Journal on Discrete Mathematics
影响因子：
0.8
作者：
Balogh J
通讯作者：
Balogh J

Sharp bounds for decomposing graphs into edges and triangles

将图分解为边和三角形的锐界

DOI：
10.1017/s0963548320000358
发表时间：
2021
期刊：
Probability and Computing
影响因子：
0
作者：
Blumenthal, Adam;Lidický, Bernard;Pehova, Yanitsa;Pfender, Florian;Pikhurko, Oleg;Volec, Jan
通讯作者：
Volec, Jan

KONIG'S LINE COLORING AND VIZING'S THEOREMS FOR GRAPHINGS

KONIG 的线着色和图形可视化定理