有理指数接近二

Q2 Mathematics

Advances in Combinatorics Pub Date : 2022-03-07 DOI:10.19086/aic.2022.9

D. Conlon, Oliver Janzer

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引用次数: 5

摘要

Erd ' s和Simonovits的一个长期猜想表明，对于1到2之间的每一个有理数r，存在一个图H，使得在n个顶点上的无H图的最大边数为Q(nr)。回答Jiang, Jiang和Ma提出的问题，我们证明了该猜想适用于所有形式为2􀀀a=b且b对a来说足够大的有理数。

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Rational Exponents Near Two

A longstanding conjecture of Erd˝os and Simonovits states that for every rational r between 1 and 2 there is a graph H such that the largest number of edges in an H-free graph on n vertices is Q(nr). Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form 2􀀀a=b with b sufficiently large in terms of a.

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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