更多关于无三角形图中的稀疏半部分

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-04-19 DOI:10.1070/SM9615

A. Razborov

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引用次数: 7

摘要

Erdős的一个猜想指出，每个顶点上的无三角形图都有一个顶点上的诱导子图，其边最多。我们报告了这个猜想的几个部分结果。特别地，我们建立了一般情况下边数的新界。完整地证明了周长图、独立数图和强正则图的猜想。这三类中的每一类都包括已知的(推测的)极值构型，5环和Petersen图。参考书目:21篇。

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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More about sparse halves in triangle-free graphs

One of Erdős’s conjectures states that every triangle-free graph on vertices has an induced subgraph on vertices with at most edges. We report several partial results towards this conjecture. In particular, we establish the new bound on the number of edges in the general case. We completely prove the conjecture for graphs of girth , for graphs with independence number and for strongly regular graphs. Each of these three classes includes both known (conjectured) extremal configurations, the 5-cycle and the Petersen graph. Bibliography: 21 titles.

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis