On equitably 2-colourable odd cycle decompositions

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2024-04-18 DOI:10.1002/jcd.21937

Andrea Burgess, Francesca Merola

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引用次数: 0

Abstract

An $ℓ$ -cycle decomposition of $K_{v}$ is said to be equitably 2-colourable if there is a 2-vertex-colouring of $K_{v}$ such that each colour is represented (approximately) an equal number of times on each cycle: more precisely, we ask that in each cycle $C$ of the decomposition, each colour appears on $⌊ ℓ ∕ 2 ⌋$ or $⌈ ℓ ∕ 2 ⌉$ of the vertices of $C$ . In this paper we study the existence of equitably 2-colourable $ℓ$ -cycle decompositions of $K_{v}$ , where $ℓ$ is odd, and prove the existence of such a decomposition for $v \equiv 1, ℓ$ (mod $2 ℓ$ ).

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关于等效 2 奇循环分解

如果存在一种 2 顶点着色，使得每种颜色在每个循环中出现的次数（近似）相等，那么我们就称这种循环分解为等效 2 顶点着色：更确切地说，我们要求在分解的每个循环中，每种颜色都出现在.的顶点或.的顶点上。本文将研究等效 2 顶点着色的循环分解的存在性，其中奇数为(mod )，并证明这种分解的存在性。

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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.