Primitive C 4 ${C}_{4}$ -decompositions of K n − I ${K}_{n}-I$

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2023-05-05 DOI:10.1002/jcd.21887

Michael W. Schroeder

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引用次数: 0

Abstract

A decomposition $C$ of a graph $G$ is primitive if no proper, nontrivial subset of $C$ is a decomposition of an induced subgraph of $G$ . An unresolved question posed by Asplund et al. in a recent publication involves the existence of primitive decompositions of cocktail party graphs into cycles of length 4, which is resolved by this paper.

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基元C4${C}_{4} Kn−I的$-分解${K}_{n}-I$

图G$G$的分解C$｛\mathscr｛C｝｝$是基元的，如果不是适当的，C$的非平凡子集是G$G$的诱导子图的分解。Asplund等人在最近的一篇出版物中提出了一个尚未解决的问题，涉及鸡尾酒会图到长度为4的循环的原始分解的存在性，本文对此进行了解决。

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

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.