AI 中文总结
本文提出定量调色板转移原理，在均匀边染色伪随机图中证明彩虹生成配置（如完美匹配、哈密顿圈、有界度生成树）的渐近几乎必然存在性，调色板大小仅比配置大小多任意小的$\n$倍。
AI 中文摘要
我们证明了均匀边染色伪随机图中彩虹生成配置的一个定量调色板转移原理。该转移原理的输入是在一个具有足够大最小度的适当双混合图$H$中嵌入生成配置的结果。转移原理的输出是，在均匀边染色的图$G$中，渐近几乎必然存在相同配置的彩虹副本，其中$G$的双混合性和最小度与$H$的相当，有时甚至重合。然后，我们应用该转移原理，在具有适当参数的双混合图中渐近几乎必然获得$K_k$-因子，包括完美匹配、哈密顿圈以及一个指定的有界度生成树。在我们所有的结果中，调色板大小超过目标配置的大小$\n$，其中$\n>0$是任意小但固定的，且$n$是配置的阶。
英文摘要
We prove a quantitative palette-transference principle for rainbow spanning configurations in uniformly edge-coloured pseudorandom graphs. The input to our transference principle is an embedding result of a spanning configuration in an appropriately bijumbled graph $H$ with sufficiently large minimum degree. The output of our transference principle is the asymptotically almost sure existence of a rainbow copy of the same configuration in a uniformly edge-coloured graph $G$ whose bijumbledness and minimum are comparable and sometimes coincide with those of $H$. We then apply our transference principle in order to asymptotically almost surely obtain $K_k$-factors, including perfect matchings, Hamilton cycles, and a prescribed bounded-degree spanning tree in bijumbled graphs with appropriate parameters. In all of our results, the palette size exceeds the size of the target configuration by $\varepsilon n$, where $\varepsilon > 0$ is arbitrarily small yet fixed, and $n$ is the order of the configuration.
CommentsCorrected one reference
