On cyclic symmetric Hamilton cycle decompositions of complete multipartite graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-08 DOI:10.1016/j.disc.2024.114277

引用次数: 0

Abstract

A decomposition of a graph with n vertices, labeled by

Z_{n}

, is cyclic if addition by 1 to the vertices acts on the decomposition, and the decomposition is d-symmetric for a divisor d of n if addition by

n / d

to the vertices acts invariantly on the decomposition. In a 2017 paper, Merola et al. established the necessary and sufficient conditions under which a complete multipartite graph with an even number of parts, each with d vertices, has a cyclic Hamilton cycle decomposition; these decompositions were also d-symmetric.

In this paper we establish the necessary and sufficient conditions for the analogous question with complete multipartite graphs with an odd number of parts, which settles the existence of cyclic, d-symmetric Hamilton cycle decompositions for all balanced, complete multipartite graphs.

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论完整多方图的循环对称汉密尔顿循环分解

一个有 n 个顶点的图的分解（用 Zn 标记），如果顶点的加法 1 作用于该分解，则该分解是循环的；如果顶点的加法 n/d 不变地作用于该分解，则该分解对于 n 的除数 d 是 d 对称的。在 2017 年的一篇论文中，Merola 等人确定了偶数部分的完整多部分图（每个部分有 d 个顶点）具有循环汉密尔顿循环分解的必要条件和充分条件；这些分解也是 d 对称的。在本文中，我们为奇数部分的完整多部分图的类似问题确定了必要条件和充分条件，从而解决了所有平衡完整多部分图的循环、d 对称汉密尔顿循环分解的存在性问题。

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.