随机超图中的匹配问题

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-10-10 DOI:10.1016/j.disc.2025.114839

Peter Frankl , Jiaxi Nie , Jian Wang

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引用次数: 0

摘要

研究了随机超图中Erdős匹配问题的一个变体。设Kp（n,k）表示有n个顶点的Erdős-Rényi随机k-均匀超图，其中每条可能的边以p的概率包含。我们证明了当n比k2s和p不太小时，具有匹配数s的Kp（n,k）的子超图的最大边数是由平凡子超图获得的，即由固定的s个顶点集合中包含至少一个顶点的所有边组成的子超图。

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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On the matching problem in random hypergraphs

We study a variant of the Erdős Matching Problem in random hypergraphs. Let

K_{p} (n, k)

denote the Erdős-Rényi random k-uniform hypergraph on n vertices where each possible edge is included with probability p. We show that when

n ≫ k^{2} s

and p is not too small, with high probability, the maximum number of edges in a sub-hypergraph of

K_{p} (n, k)

with matching number s is obtained by the trivial sub-hypergraphs, i.e. the sub-hypergraph consisting of all edges containing at least one vertex in a fixed set of s vertices.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.