AI 中文总结
该研究将Erdős与Gyárfás的单色路径覆盖猜想推广到单色环覆盖，证明n顶点完全图的任意2边着色都存在至多⌈√n⌉个同色单色环覆盖所有顶点，且该界阶最优、向上取整对无穷多n必要。
AI 中文摘要
我们将Erdős和Gyárfás关于单色路径覆盖的猜想推广到单色环覆盖的情形，证明对所有n，n顶点完全图的任意2边着色都包含一组至多⌈√n⌉个同色单色环，可覆盖所有顶点，该界的阶是最优的，且对无穷多n而言，向上取整是必要的。
英文摘要
We extend the conjecture of Erdős and Gyárfás on monochromatic path covers to the setting of monochromatic cycle covers. We prove that, for all $n$, every 2-edge-coloring of the complete graph on $n$ vertices contains a collection of at most $\lceil\sqrt{n}\rceil$ monochromatic cycles, all of the same color, that together cover all vertices. The order of the bound is best possible, and the ceiling is necessary for infinitely many $n$.
Comments16 pages
