Packing of the k-power of Hamilton cycles

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-11 DOI:10.1016/j.disc.2025.114630

Wanfang Chen, Changhong Lu, Qi Wu, Long-Tu Yuan

引用次数: 0

Abstract

The k-power of a Hamilton cycle is obtained from it by adding edges between all two vertices whose distance in it is at most k. For sufficiently large n, we determine the maximum number of edges of an n-vertex graph without containing the k-power of a Hamilton cycle, and identify all n-vertex graphs with at most

n - 2 k + ℓ

edges which do not pack with the k-power of a Hamilton cycle.

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汉密尔顿环的k-幂的包装

Hamilton环的k次幂是通过在其中距离不超过k的所有两个顶点之间添加边而得到的。对于足够大的n，我们确定了不包含Hamilton环k次的n顶点图的最大边数，并确定了所有不包含Hamilton环k次的n顶点图的最多n−2k+ l条边。

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 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.