Finitely forcible graphons with an almost arbitrary structure

IF 1 3区数学 Q1 MATHEMATICS

Discrete Analysis Pub Date : 2018-09-16 DOI:10.19086/DA.12058

D. Král, L. Lov'asz, Jonathan A. Noel, Jakub Sosnovec

引用次数: 3

Abstract

A basic result from the theory of quasirandom graphs, due to Andrew Thomason, is that if is a graph with vertices and density , and if the number of 4-cycles in is approximately , then resembles a random graph of the same density. In particular, between any two sets and of vertices the number of edges is approximately . (Here, “approximately” means "to within a small fraction of , so the statement is non-trivial only for sets and that are not too small.)

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具有几乎任意结构的有限强制图

由Andrew Thomason提出的准随机图理论的一个基本结果是，如果是一个具有顶点和密度的图，并且如果中的4个循环的数量近似，则类似于具有相同密度的随机图。特别地，在任意两个集合和顶点之间，边的数量近似。（这里，“近似”的意思是“在的一小部分内，因此该语句仅对不太小的集合是非平凡的。）

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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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.