On Powers of Hamilton Cycles in Ramsey–Turán Theory

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-09-16 DOI:10.1137/24m163709x

Ming Chen, Jie Han, Yantao Tang, Donglei Yang

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2489-2508, September 2024.
Abstract. We prove that for [math] with [math] and [math], there exist [math] and [math] such that for every [math], every [math]-vertex graph [math] with [math] and [math] contains an [math]th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for [math] and the [math] case was recently conjectured by Staden and Treglown.

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论拉姆齐-图兰理论中的汉密尔顿循环幂

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2489-2508 页，2024 年 9 月。摘要。我们证明，对于具有[math]和[math]的[math]，存在[math]和[math]，使得对于每一个[math]，具有[math]和[math]的每一个[math]顶点图[math]都包含一个汉密尔顿循环的[math]次方。我们还证明，对于[math]和[math]的[math]情况，最小度条件是渐近尖锐的，而[math]的情况是 Staden 和 Treglown 最近猜想出来的。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.