对于随机完美图，一阶收敛律失效

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.013

Tobias Müller, Marc Noy

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引用次数: 0

摘要

研究了随机完美图的一阶可表达性质。也就是说，我们从n个顶点上的所有(标记的)完美图中均匀随机地选择一个图Gn，并考虑它满足一些可以用图的一阶语言表示的图性质的概率。我们证明了存在这样一个一阶可表达性，使得Gn满足它的概率不收敛于n→∞。

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The first order convergence law fails for random perfect graphs

We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_{n}$ uniformly at random from all (labelled) perfect graphs on n vertices and consider the probability that it satisfies some graph property that can be expressed in the first order language of graphs. We show that there exists such a first order expressible property for which the probability that $G_{n}$ satisfies it does not converge as $n \to \infty$ .

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.