Extremal combinatorics and asymptotic enumeration

极值组合和渐近枚举

• 批准号: EP/I026630/1
• 负责人: Jan Hladky
• 金额: $ 27.97万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI026630%2F1
• 关键词: Extremal; combinatorics; asymptotic; enumeration

Combinatorics is a branch of mathematics studying finite structures. The generality of these questions suggests wide applicability of combinatorics in other areas of pure mathematics (most notably in algebra, number theory, probability, and topology), as well as in real-world applications (discrete optimization, computer science).One of the oldest and most central parts of combinatorics are graph theory and enumerative combinatorics. Graph theory models networks (such as road connections, or internet users), and enumerative combinatorics concerns studying counting questions of various kinds.Extremal graph theory is a broad part of graph theory which investigates interplay between various graph parameters. One of the main tools in Extremal graph theory is the so-called Szemeredi Regularity Lemma. This tool (developed in the 70's) has become one of the corner-stones of modern mathematics. Recently, using the insights gained from the Regularity Lemma, Lovasz and Szegedy initiated study of graph limits.The proposed research project addresses major open questions in extremal graph theory and aims contribute to general theories the Regularity Lemma, graph limits, and by developing novel tools which will be used in enumerative combinatorics.

组合学是研究有限结构的数学分支。这些问题的普遍性表明组合数学在纯数学的其他领域（尤其是代数、数论、概率和拓扑）以及现实世界的应用（离散优化、计算机科学）中具有广泛的适用性。组合数学最古老和最核心的部分之一是图论和枚举组合数学。图论对网络（例如道路连接或互联网用户）进行建模，而枚举组合学涉及研究各种计数问题。极值图论是图论的一个广泛部分，它研究各种图参数之间的相互作用。极值图论的主要工具之一是所谓的 Szemeredi 正则引理。这个工具（于 70 年代开发）已成为现代数学的基石之一。最近，利用从正则引理中获得的见解，Lovasz 和 Szegedy 启动了图极限的研究。拟议的研究项目解决了极值图论中的主要开放问题，旨在为正则引理、图极限的一般理论做出贡献，并开发用于枚举组合学的新颖工具。

项目成果

Chromatic roots and limits of dense graphs

• DOI: 10.1016/j.disc.2016.11.009
• 发表时间: 2015-11
• 期刊: Discret. Math.
• 作者: P. Csikvári;P. Frenkel;J. Hladký;T. Hubai

POSET LIMITS CAN BE TOTALLY ORDERED

POSET 限制可以完全排序

• 发表时间: 2015
• 期刊: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• 影响因子: 1.3
• 作者: Hladky Jan

DENSE FLAG TRIANGULATIONS OF 3-MANIFOLDS VIA EXTREMAL GRAPH THEORY

基于极值图论的三流形密集旗三角剖分

• 发表时间: 2015
• 期刊: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• 影响因子: 1.3
• 作者: Adamaszek Michal

Hamilton cycles in dense vertex-transitive graphs

密集顶点传递图中的哈密顿循环

• DOI: 10.1016/j.jctb.2014.05.001
• 发表时间: 2014
• 期刊: Journal of Combinatorial Theory, Series B
• 作者: Christofides D

An extension of Turan's Theorem, uniqueness and stability

图兰定理的延伸，唯一性和稳定性

• 发表时间: 2014
• 期刊: ELECTRONIC JOURNAL OF COMBINATORICS
• 影响因子: 0.7
• 作者: Allen Peter