随机超图中紧汉密尔顿环幂的阈值

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-02 DOI:10.1016/j.disc.2025.114599

Yulin Chang , Jie Han , Lin Sun

引用次数: 0

摘要

研究了随机超图中紧汉密尔顿环幂的出现。对于每一个r≥3和k≥1，我们证明存在一个常数C>；0，使得当p=p(n)≥Cn−1/(k+r−2r−1)，则随机超图H(r)（n,p）渐近几乎肯定包含紧汉密尔顿环的k次幂。这改进了parzyk和Person的结果，他们在p=ω(n−1/(k+r−2r−1))的假设下使用第二矩论证证明了相同的结果。

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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The threshold for powers of tight Hamilton cycles in random hypergraphs

We investigate the occurrence of powers of tight Hamilton cycles in random hypergraphs. For every

r \geq 3

and

k \geq 1

, we show that there exists a constant

C > 0

such that if

p = p (n) \geq C n^{- 1 / (\begin{matrix} k + r - 2 \\ r - 1 \end{matrix})}

then asymptotically almost surely the random hypergraph

H^{(r)} (n, p)

contains the kth power of a tight Hamilton cycle. This improves on a result of Parczyk and Person, who proved the same result under the assumption

p = ω (n^{- 1 / (\begin{matrix} k + r - 2 \\ r - 1 \end{matrix})})

using a second moment argument.

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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.