完成了等长环有向Oberwolfach问题的求解

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2023-09-25 DOI:10.1002/jcd.21918

Alice Lacaze-Masmonteil

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引用次数: 3

摘要

本文给出了具有等长表的有向Oberwolfach问题的最后一个突出情况的解。也就是说，我们用奇数长度相等的表来处理双表的情况。我们证明了2m$ 2m$顶点上的完全对称有向图，记作K 2m * ${K}_{2m}^{*}$，允许分解成奇数长度m$ m$的有向环。这完全解决了等长表的有向奥伯沃尔法赫问题。

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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Completing the solution of the directed Oberwolfach problem with cycles of equal length

In this paper, we give a solution to the last outstanding case of the directed Oberwolfach problem with tables of uniform length. Namely, we address the two-table case with tables of equal odd length. We prove that the complete symmetric digraph on $2 m$ vertices, denoted $K_{2 m}^{*}$ , admits a resolvable decomposition into directed cycles of odd length $m$ . This completely settles the directed Oberwolfach problem with tables of uniform length.

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.