Lehel猜想的彩虹版本
A rainbow version of Lehel's conjecture
AI总结：
本文研究恰当边着色完全图背景下Lehel猜想的彩虹类似问题，证明足够大的n时，恰当边着色K_n的顶点集可划分为两个顶点不相交的彩虹圈。
AI中文摘要：
Lehel猜想指出，完全图K_n的任意2边着色都允许将其顶点集划分为两个单色圈。该猜想在n足够大时于1998年被Łuczak、Rödl和Szemerédi证明，2008年Allen对其进行了改进，2010年Bessy和Thomassé完全解决了该猜想。本文在恰当边着色的完全图背景下考虑Lehel猜想的彩虹类似问题，证明对于足够大的n，每一个恰当边着色的K_n都允许将其顶点集划分为两个顶点不相交的彩虹圈。
英文摘要：
Lehel's conjecture states that every 2-edge-colouring of K_n admits a partition of its vertex set into two monochromatic cycles. It was proven for sufficiently large n by Łuczak, Rödl, and Szemerédi in 1998, later improved by Allen in 2008, and fully resolved by Bessy and Thomassé in 2010. In this paper, we consider a rainbow analogue of Lehel's conjecture in the setting of properly edge-coloured complete graphs. We prove that, for sufficiently large n, every properly edge-coloured Kn admits a partition of its vertex set into two vertex-disjoint rainbow cycles
