Turán定理的精确稳定性

Q2 Mathematics

Advances in Combinatorics Pub Date : 2020-04-22 DOI:10.19086/aic.31079

D'aniel Kor'andi, Alexander Roberts, A. Scott

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引用次数: 11

摘要

Turán定理指出一个极值Kr+1自由图是r部分图。Erdõs和Simonovits的稳定性定理表明，如果一个具有n个顶点的Kr+1自由图具有接近于最大tr（n）边的边，则它接近于r部分。在本文中，对于任意m≥tr（n）-δrn2，我们精确地确定了具有至少m条边的Kr+1自由图，这些边离r部分最远。这扩展了Erdõs、Gyõri和Simonovits的工作，并证明了Balogh、Clemen、Lavrov、Lidický和Pfender的一个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exact stability for Turán’s Theorem

Turán's Theorem says that an extremal Kr+1-free graph is r-partite. The Stability Theorem of Erdős and Simonovits shows that if a Kr+1-free graph with n vertices has close to the maximal tr(n) edges, then it is close to being r-partite. In this paper we determine exactly the Kr+1-free graphs with at least m edges that are farthest from being r-partite, for any m≥tr(n)−δrn2. This extends work by Erdős, Győri and Simonovits, and proves a conjecture of Balogh, Clemen, Lavrov, Lidický and Pfender.

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来源期刊

Advances in Combinatorics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

3.10

自引率

0.00%

发文量