A note on rainbow stackings of random edge-colorings of hypergraphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-19 DOI:10.1016/j.disc.2024.114261

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引用次数: 0

Abstract

A rainbow stacking of r-edge-colorings $χ_{1}, \dots, χ_{m}$ of the complete d-uniform hypergraph on n vertices is a way of superimposing $χ_{1}, \dots, χ_{m}$ so that no edges of the same color are superimposed on each other. The definition of rainbow stackings of graphs was proposed by Alon, Defant, and Kravitz, and they determined a sharp threshold for r (as a function of m and n) governing the existence and nonexistence of rainbow stackings of random r-edge-colorings $χ_{1}, \dots, χ_{m}$ of the complete graph $K_{n}$ . In this paper, we extend their result to d-uniform hypergraph, obtain a sharp threshold for r controlling the existence and nonexistence of rainbow stackings of random r-edge-colorings $χ_{1}, \dots, χ_{m}$ of the complete d-uniform hypergraph for $d \geq 3$ .

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关于超图随机边着色的彩虹堆积的说明

n 个顶点上的完整 d-Uniform 超图的 r 边颜色 χ1，...，χm 的彩虹叠加是一种叠加 χ1，...，χm 的方法，这样就不会有相同颜色的边相互叠加。图的彩虹叠加定义是由 Alon、Defant 和 Kravitz 提出的，他们确定了 r 的一个尖锐临界值（作为 m 和 n 的函数），该临界值决定了完整图 Kn 的随机 r 边颜色χ1,...,χm 的彩虹叠加存在与否。在本文中，我们将他们的结果推广到 d-uniform hypergraph，得到了一个控制完整 d-uniform hypergraph 的随机 r 边着色 χ1,...,χm 的彩虹堆叠存在与否的 r 的尖锐阈值，且 d≥3 时。

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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.