随机边缘颜色的彩虹堆叠

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-13 DOI:10.1112/blms.70052

Noga Alon, Colin Defant, Noah Kravitz

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引用次数: 0

摘要

r$ r$ -边颜色的彩虹堆叠χ 1，…，χ m $\chi _1, \ldots，n$ n$顶点上的完全图的\chi _m$是一种叠加χ 1，…，χ m$ \chi _1, \ldots，\chi _m$，以便没有相同颜色的边缘相互重叠。我们确定了r$ r$的一个尖锐阈值（作为m$ m$和n$ n$的函数）来控制随机r$ r$ -边着色χ 1的彩虹堆叠的存在性和不存在性， χ m$ \chi _1,\ldots,\chi _m$。

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Rainbow stackings of random edge-colorings

A rainbow stacking of $r$ -edge-colorings $χ_{1}, …, χ_{m}$ of the complete graph on $n$ vertices is a way of superimposing $χ_{1}, …, χ_{m}$ so that no edges of the same color are superimposed on each other. We determine 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 $χ_{1}, …, χ_{m}$ .